Bartleby Sitemap - Textbook Solutions
All Textbook Solutions for Precalculus
Satellite Dish A satellite dish is shaped like a paraboloid of revolution. The signals that emanate from a satellite strike the surface of the dish and are reflected to a single point, where the receiver is located. If the dish is 10 feet across at its opening and 4 feet deep at its center, at what position should the receiver be placed?64AYU65AYU66AYU67AYU68AYU69AYU70AYU71AYU72AYU73AYU74AYU75AYU76AYU77AYU78AYU79AYUThe distance d from P 1 =( 2,5 ) to P 2 =( 4,2 ) is d= ______. (p.4)To complete the square of x 2 3x , Add _____. (p. A28-A29)Find the intercepts of the equation y 2 =164 x 2 . (pp. 18-19)The point that is symmetric with respect to the y-axis to the point ( 2,5 ) is ________. (pp. 19-21)The point that is symmetric with respect to the y-axis to the point ( 2,5 ) is _______. (pp. 19-21)6AYUA(n) _______ is the collection of all points in a plane the sum of whose distances from two fixed points is a constant.Multiple Choice For an ellipse, the foci lie on a line called the _________.
Minor axis
Major axis
Directrix
Latus rectum
For the ellipse x 2 4 + y 2 25 =1 , the vertices are the points _______ and _______.For the ellipse x 2 25 + y 2 9 =1 , the value of a is ______, the value of b is ______, and the major axis is the ______ -axis.If the center of an ellipse is ( 2,3 ) , the major axis is parallel to the x-axis , and the distance from the center of the ellipse to its vertices is a=4 units, then the coordinates of the vertices are _______ and _______.12AYUIn problems 13-16, the graph of an ellipse is given. Match each graph to its equation. (A) x 2 4 + y 2 =1 (B) x 2 + y 2 4 =1 (C) x 2 16 + y 2 4 =1 (D) x 2 4 + y 2 16 =1In problems 13-16, the graph of an ellipse is given. Match each graph to its equation. (A) x 2 4 + y 2 =1 (B) x 2 + y 2 4 =1 (C) x 2 16 + y 2 4 =1 (D) x 2 4 + y 2 16 =1In problems 13-16, the graph of an ellipse is given. Match each graph to its equation. (A) x 2 4 + y 2 =1 (B) x 2 + y 2 4 =1 (C) x 2 16 + y 2 4 =1 (D) x 2 4 + y 2 16 =1In problems 13-16, the graph of an ellipse is given. Match each graph to its equation. (A) x 2 4 + y 2 =1 (B) x 2 + y 2 4 =1 (C) x 2 16 + y 2 4 =1 (D) x 2 4 + y 2 16 =1In Problems 1726, analyze each equation. That is, find the center, vertices, and foci of each ellipse and graph it. x225+y24=1In Problems analyze each equation. That is, find the center, vertices, and foci of each ellipse and graph it.
In Problems analyze each equation. That is, find the center, vertices, and foci of each ellipse and graph it.
In Problems 1726, analyze each equation. That is, find the center, vertices, and foci of each ellipse and graph it. x2+y216=1In Problems 1726, analyze each equation. That is, find the center, vertices, and foci of each ellipse and graph it. 4x2+y2=16In Problems analyze each equation. That is, find the center, vertices, and foci of each ellipse and graph it.
In Problems analyze each equation. That is, find the center, vertices, and foci of each ellipse and graph it.
In Problems analyze each equation. That is, find the center, vertices, and foci of each ellipse and graph it.
In Problems analyze each equation. That is, find the center, vertices, and foci of each ellipse and graph it.
In Problems 1726, analyze each equation. That is, find the center, vertices, and foci of each ellipse and graph it. x2+y2=4In Problems 27-38, find an equation for each ellipse. Graph the equation by hand. Center at ( 0,0 ) ; focus at ( 3,0 ) ; vertex at ( 5,0 )In Problems 27-38, find an equation for each ellipse. Graph the equation by hand. Center at ( 0,0 ) ; focus at ( 1,0 ) ; vertex at ( 3,0 )In Problems 27-38, find an equation for each ellipse. Graph the equation by hand. Center at ( 0,0 ) ; focus at ( 0,4 ) ; vertex at ( 0,5 )In Problems 27-38, find an equation for each ellipse. Graph the equation by hand. Center at ( 0,0 ) ; focus at ( 0,1 ) ; vertex at ( 0,2 )In Problems 27-38, find an equation for each ellipse. Graph the equation by hand. Foci at ( 2,0 ) ; length of the major axis is 6In Problems 27-38, find an equation for each ellipse. Graph the equation by hand. Foci at ( 0,2 ) ; length of the major axis is 8In Problems 27-38, find an equation for each ellipse. Graph the equation by hand. Focus at ( 4,0 ) ; vertices at ( 5,0 )In Problems 27-38, find an equation for each ellipse. Graph the equation by hand. Focus at ( 0,4 ) ; vertices at ( 0,8 )In Problems 27-38, find an equation for each ellipse. Graph the equation by hand. Foci at ( 0,3 ) ; x-intercepts are 2In Problems 27-38, find an equation for each ellipse. Graph the equation by hand. Vertices at ( 4,0 ) ; y-intercepts are 1In Problems 27-38, find an equation for each ellipse. Graph the equation by hand. Center at ( 0,0 ) ; vertex at ( 0,4 ) ; b=1In Problems 27-38, find an equation for each ellipse. Graph the equation by hand. Vertices at ( 5,0 ) ; c=2In Problems 39-42, write an equation for each ellipse.In Problems 39-42, write an equation for each ellipse.In Problems 39-42, write an equation for each ellipse.In Problems 39-42, write an equation for each ellipse.In Problems analyze each equationthat is, find the center, foci, and vertices of each ellipse. Graph each equation.
In Problems 4354, analyze each equation ; that is, find the center, foci, and vertices of each ellipse. Graph each equation. (x+4)29+(y+2)24=1In Problems analyze each equationthat is, find the center, foci, and vertices of each ellipse. Graph each equation.
In Problems 4354, analyze each equation ; that is, find the center, foci, and vertices of each ellipse. Graph each equation. 9(x3)2+(y+2)2=18In Problems 4354, analyze each equation ; that is, find the center, foci, and vertices of each ellipse. Graph each equation. x2+4x+4y28y+4=0In Problems analyze each equationthat is, find the center, foci, and vertices of each ellipse. Graph each equation.
In Problems 4354, analyze each equation ; that is, find the center, foci, and vertices of each ellipse. Graph each equation. 2x2+3y28x+6y+5=0In Problems 4354, analyze each equation ; that is, find the center, foci, and vertices of each ellipse. Graph each equation. 4x2+3y2+8x6y=5In Problems analyze each equationthat is, find the center, foci, and vertices of each ellipse. Graph each equation.
In Problems 4354, analyze each equation ; that is, find the center, foci, and vertices of each ellipse. Graph each equation. x2+9y2+6x18y+9=0In Problems 4354, analyze each equation ; that is, find the center, foci, and vertices of each ellipse. Graph each equation. 4x2+y2+4y=0In Problems analyze each equationthat is, find the center, foci, and vertices of each ellipse. Graph each equation.
In Problems 5564, find an equation for each ellipse. Graph the equation. Center at (2,2); vertex at (7,2) ; focus at (4,2)In Problems , find an equation for each ellipse. Graph the equation.
Center at vertex at focus at
In Problems , find an equation for each ellipse. Graph the equation.
Vertices at and focus at
In Problems 5564, find an equation for each ellipse. Graph the equation. Foci at (1,2) and (3,2) ; vertex at (4,2)In Problems 5564, find an equation for each ellipse. Graph the equation. Foci at (5,1) and (1,1) ; length of the major axis is 8.In Problems 5564, find an equation for each ellipse. Graph the equation. Vertices at (2,5) and (2,1);c=2In Problems , find an equation for each ellipse. Graph the equation.
Center at focus at contains the point
In Problems 5564, find an equation for each ellipse. Graph the equation. Center at (1,2); focus at (1,4); contains the point (2,2)In Problems 5564, find an equation for each ellipse. Graph the equation. Center at (1,2); vertex at (4,2); contains the point (1,5)In Problems , find an equation for each ellipse. Graph the equation.
Center at vertex at contains the point
In Problems 65-68, graph each function. Be sure to label all the intercepts. [ Hint: Notice that each function is half an ellipse.] f( x )= 164 x 2In Problems 65-68, graph each function. Be sure to label all the intercepts. [ Hint: Notice that each function is half an ellipse.] f( x )= 99 x 2In Problems 65-68, graph each function. Be sure to label all the intercepts. [ Hint: Notice that each function is half an ellipse.] f( x )= 6416 x 2In Problems 65-68, graph each function. Be sure to label all the intercepts. [ Hint: Notice that each function is half an ellipse.] f( x )= 44 x 2Semielliptical Arch Bridge An arch in the shape of the upper half of an ellipse is used to support a bridge that is to span a river 20 meters wide. The center of the arch is 6 meters above the center of the river. See the figure. Write an equation for the ellipse in which the x-axis coincides with the water level and the y-axis passes through the center of the arch.Semielliptical Arch Bridge The arch of a bridge is a semiellipse with a horizontal major axis. The span is 30 feet, and the top of the arch is 10 feet above the major axis. The roadway is horizontal and is 2 feet above the top of the arch. Find the vertical distance from the roadway to the arch at 5-foot intervals along the roadway.Whispering Gallery A hall 100 feet in length is to be designed as a whispering gallery. If the foci are located 25 feet from the center, how high will the ceiling be at the center?Whispering Gallery Jim, standing at one focus of a whispering gallery, is 6 feet from the nearest wall. His friend is standing at the other focus, 100 feet away. What is the length of this whispering gallery? How high is its elliptical ceiling at the center?Semielliptical Arch Bridge A bridge is built in the shape of a semielliptical arch. The bridge has a span of 120 feet and a maximum height of 25 feet. Choose a suitable rectangular coordinate system and find the height of the arch at distances of 10, 30, and 50 feet from the center.Semielliptical Arch Bridge A bridge is to be built in the shape of a semielliptical arch and is to have a span of 100 feet. The height of the arch, at a distance of 40 feet from the center, is to be 10 feet. Find the height of the arch at its center.Racetrack Design Consult the figure. A racetrack is in the shape of an ellipse, 100 feet long and 50 feet wide. What is the width 10 feet from a vertex?Semielliptical Arch Bridge An arch for a bridge over a highway is in the form of half an ellipse. The top of the arch is 20 feet above the ground level (the major axis). The highway has four lanes, each 12 feet wide; a center safety strip 8 feet wide; and two side strips, each 4 feet wide. What should the span of the bridge be (the length of its major axis) if the height 28 feet from the center is to be 13 feet?Installing a Vent Pipe A homeowner is putting in a fireplace that has a 4-inch-radius vent pipe. He needs to cut an elliptical hole in his roof to accommodate the pipe. If the pitch of his roof is 5 4 , (a rise of 5, run of 4) what are the dimensions of the hole?Semielliptical Arch Bridge An arch for a bridge over a highway is in the form of half an ellipse. The top of the arch is 20 feet above the ground level (the major axis). The highway has four lanes, each 12 feet wide; a center safety strip 8 feet wide; and two side strips, each 4 feet wide. What should the span of the bridge be (the length of its major axis) if the height 28 feet from the center is to be 13 feet?In Problems 79-83, use the fact that the orbit of a planet about the Sun is an ellipse, with the Sun at one focus. The aphelion of a planet is its greatest distance from the Sun, and the perihelion is its shortest distance. The mean distance of a planet from the Sun is the length of the semimajor axis of the elliptical orbit. See the illustration. Earth The mean distance of Earth from the Sun is 93 million miles. If the aphelion of Earth is 94.5 million miles, what is the perihelion? Write an equation for the orbit of Earth around the Sun.In Problems 79-83, use the fact that the orbit of a planet about the Sun is an ellipse, with the Sun at one focus. The aphelion of a planet is its greatest distance from the Sun, and the perihelion is its shortest distance. The mean distance of a planet from the Sun is the length of the semimajor axis of the elliptical orbit. See the illustration. Mars The mean distance of Mars from the Sun is 142 million miles. If the perihelion of Mars is 128.5 million miles, what is the aphelion? Write an equation for the orbit of Mars about the Sun.In Problems 79-83, use the fact that the orbit of a planet about the Sun is an ellipse, with the Sun at one focus. The aphelion of a planet is its greatest distance from the Sun, and the perihelion is its shortest distance. The mean distance of a planet from the Sun is the length of the semimajor axis of the elliptical orbit. See the illustration. Mars The mean distance of Mars from the Sun is 142 million miles. If the perihelion of Mars is 128.5 million miles, what is the aphelion? Write an equation for the orbit of Mars about the Sun.In Problems 79-83, use the fact that the orbit of a planet about the Sun is an ellipse, with the Sun at one focus. The aphelion of a planet is its greatest distance from the Sun, and the perihelion is its shortest distance. The mean distance of a planet from the Sun is the length of the semimajor axis of the elliptical orbit. See the illustration. Pluto The perihelion of Pluto is 4551 million miles, and the distance from the center of its elliptical orbit to the Sun is 897.5 million miles. Find the aphelion of Pluto. What is the mean distance of Pluto from the Sun? Write an equation for the orbit of Pluto about the Sun.83AYU84AYU85AYUThe distance d from P 1 =( 2,5 ) to P 2 =( 4,2 ) is d= _____. (p. 4)2AYU3AYU4AYU5AYU6AYUA(n) _______ is the collection of points in a plane the difference of whose distances from two fixed points is a constant.For a hyperbola, the foci lie on a line called the ________.Answer Problems 9-11 using the figure to the right. The equation of the hyperbola is of the form (a) ( xh ) 2 a 2 ( yk ) 2 b 2 =1 (b) ( yk ) 2 a 2 ( xh ) 2 b 2 =1 (c) ( xh ) 2 a 2 + ( yk ) 2 b 2 =1 (d) ( xh ) 2 b 2 + ( yk ) 2 a 2 =1Answer Problems 9-11 using the figure to the right. If the center of the hyperbola is ( 2,1 ) and a=3 , then the coordinates of the vertices are _______ and _________.Answer Problems 9-11 using the figure to the right. If the center of the hyperbola is ( 2,1 ) and c=5 , then the coordinates of the foci are _______ and _________.In a hyperbola, if a=3 and c=5 , then b= ________. (a) 1(b) 2(c) 4(d) 8For the hyperbola x 2 4 y 2 9 =1 , the value of a is _______, the value of b is _____, and the transverse axis is the _____ -axis .For the hyperbola y 2 16 x 2 81 =1 , the asymptotes are ________ and _________.In Problems 15-18, the graph of a hyperbola is given. Match each graph to its equation. (A) x 2 4 y 2 =1 (B) x 2 y 2 4 =1 (C) y 2 4 x 2 =1 (D) y 2 x 2 4 =1In Problems 15-18, the graph of a hyperbola is given. Match each graph to its equation. (A) x 2 4 y 2 =1 (B) x 2 y 2 4 =1 (C) y 2 4 x 2 =1 (D) y 2 x 2 4 =1In Problems 15-18, the graph of a hyperbola is given. Match each graph to its equation. (A) x 2 4 y 2 =1 (B) x 2 y 2 4 =1 (C) y 2 4 x 2 =1 (D) y 2 x 2 4 =1In Problems 15-18, the graph of a hyperbola is given. Match each graph to its equation. (A) x 2 4 y 2 =1 (B) x 2 y 2 4 =1 (C) y 2 4 x 2 =1 (D) y 2 x 2 4 =1In Problems 1928, find an equation for the hyperbola described. Graph the equation. Center at (0,0); focus at (3,0); vertex at (1,0)In Problems 1928, find an equation for the hyperbola described. Graph the equation. Center at (0,0); focus at (0,5); vertex at (0,3)In Problems, find an equation for the hyperbola described. Graph the equation.
Center at ; focus at ; vertex at
In Problems, find an equation for the hyperbola described. Graph the equation.
Center at ; focus at ; vertex at
In Problems, find an equation for the hyperbola described. Graph the equation.
Foci at and ; vertex at
In Problems, find an equation for the hyperbola described. Graph the equation.
Focus at ; vertices at and .
In Problems, find an equation for the hyperbola described. Graph the equation.
Vertices at and ; asymptote the line .
In Problems 1928, find an equation for the hyperbola described. Graph the equation. Vertices at (4,0) and (4,0); asymptote the line y=2x.In Problems 1928, find an equation for the hyperbola described. Graph the equation. Foci at (4,0) and (4,0); asymptote the line y=x.In Problems 1928, find an equation for the hyperbola described. Graph the equation. Foci at (0,2) and (0,2); asymptote the line y=x.In Problems, find the center , transverse axis, vertices, foci and asymptotes. Graph each equation.
In Problems, find the center , transverse axis, vertices, foci and asymptotes. Graph each equation.
In Problems 2936, find the center, transverse axis, vertices, foci and asymptotes. Graph each equation. 4x2y2=16In Problems 2936, find the center, transverse axis, vertices, foci and asymptotes. Graph each equation. 4y2x2=16In Problems, find the center, transverse axis, vertices, foci and asymptotes. Graph each equation.
In Problems 2936, find the center, transverse axis, vertices, foci and asymptotes. Graph each equation. x2y2=4.In Problems, find the center, transverse axis, vertices, foci and asymptotes. Graph each equation.
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In Problems 2936, find the center, transverse axis, vertices, foci and asymptotes. Graph each equation. 2x2y2=4.In Problems 37-40, write an equation for each hyperbola.In Problems 37-40, write an equation for each hyperbola.In Problems 37-40, write an equation for each hyperbola.In Problems 37-40, write an equation for each hyperbola.In Problems 41-48, find an equation for the hyperbola described. Graph the equation by hand. Center at (4,1) ; focus at (7,1) ; vertex at (6,1)In Problems 41-48, find an equation for the hyperbola described. Graph the equation by hand. Center at (3,1) ; focus at (3,6) ; vertex at (3,4)In Problems 41-48, find an equation for the hyperbola described. Graph the equation by hand. Center at (3,4) ; focus at (3,8) ; vertex at (3,2)In Problems 41-48, find an equation for the hyperbola described. Graph the equation by hand. Center at (1,4) ; focus at (2,4) ; vertex at (0,4)In Problems 41-48, find an equation for the hyperbola described. Graph the equation by hand. Foci at (3,7) ; and (7,7) ; vertex at (6,7)In Problems 41-48, find an equation for the hyperbola described. Graph the equation by hand. Focus at (4,0) ; vertices at (4,4) ; and (4,2)In Problems 41-48, find an equation for the hyperbola described. Graph the equation by hand. Vertices at (1,1) ; and (3,1) ; asymptote the line y+1= 3 2 (x1)In Problems 41-48, find an equation for the hyperbola described. Graph the equation by hand. Vertices at (1,3) ; and (1,1) ; asymptote the line y+1= 3 2 (x1)In Problems 4962, find the center, transverse axis, vertices, foci and asymptotes. Graph each equation. (x2)24(y+3)29=1.In Problems, find the center, transverse axis, vertices, foci and asymptotes. Graph each equation.
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In Problems, find the center, transverse axis, vertices, foci and asymptotes. Graph each equation.
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In Problems 4962, find the center, transverse axis, vertices, foci and asymptotes. Graph each equation. (x+4)29(y3)2=9.In Problems 4962, find the center, transverse axis, vertices, foci and asymptotes. Graph each equation. (x+1)2(y+2)2=4.In Problems, find the center, transverse axis, vertices, foci and asymptotes. Graph each equation.
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In Problems, find the center, transverse axis, vertices, foci and asymptotes. Graph each equation.
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In Problems, find the center, transverse axis, vertices, foci and asymptotes. Graph each equation.
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In Problems 4962, find the center, transverse axis, vertices, foci and asymptotes. Graph each equation. y24x24y8x4=0.In Problems 4962, find the center, transverse axis, vertices, foci and asymptotes. Graph each equation. 2x2y2+4x+4y4=0.In Problems, find the center, transverse axis, vertices, foci and asymptotes. Graph each equation.
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In Problems 4962, find the center, transverse axis, vertices, foci and asymptotes. Graph each equation. 2y2x2+2x+8y+3=0.In Problems, find the center, transverse axis, vertices, foci and asymptotes. Graph each equation.
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In Problems, find the center, transverse axis, vertices, foci and asymptotes. Graph each equation.
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63AYU64AYU65AYU66AYU67AYU68AYU69AYU70AYU71AYU72AYU73AYU74AYUFireworks Display Suppose that two people standing 2 miles apart both see the burst from a fireworks display. After a period of time the first person, standing at point A , hears the burst. One second later the second person, standing at point B , hears the burst. If the person at point B is due west of the person at point A , and if the display is known to occur due north of the person at point A , where did the fireworks display occur?Lightning Strikes Suppose that two people standing 1 mile apart both see a flash of lightning. After a period of time the first person, standing at point A , hears the thunder. Two seconds later the second person, standing at point B , hears the thunder. If the person at point B is due west of the person at point A , and if the lightning strike is known to occur due north of the person standing at point A , where did the lightning strike occur?Nuclear Power Plaut Some nuclear power plants utilize “natural draft� cooling towers in the shape of a hyperboloid, a solid obtained by rotating a hyperbola about its conjugate axis. Suppose that such a cooling tower has a base diameter of 400 feet and the diameter at its narrowest point, 360 feet above the ground, is 200 feet. If the diameter at the top of the tower is 300 feet, how tall is the tower? Source: Bay Area Air Quality Management District78AYURutherford’s Experiment In May 1911, Ernest Rutherford published a paper in Philosophical Magazine. In this article, he described the motion of alpha particles as they are shot at a piece of gold foil 0.00004 cm thick. Before conducting this experiment, Rutherford expected that the alpha particles would shoot through the foil just as a bullet would shoot through snow. Instead, a small fraction of the alpha particles bounced off the foil. This led to the conclusion that the nucleus of an atom is dense, while the remainder of the atom is sparse. Only the density of the nucleus could cause the alpha particles to deviate from their path. The figure shows a diagram from Rutherford’s paper that indicates that the deflected alpha particles follow the path of one branch of a hyperbola. (a) Find an equation of the asymptotes under this scenario. (b) If the vertex of the path of the alpha particles is 10 cm from the center of the hyperbola, find a model that describes the path of the particle.80AYU81AYU82AYU83AYU84AYU85AYU86AYUThe sum formula for the sine function is sin( A+B )= . (p.493)The Double-angle Formula for the sine function is sin( 2 )= . (p.503)If is acute, the Half-angle Formula for the sine function is sin 2 = . (p.506)If is acute, the Half-angle Formula for the cosine function is cos 2 = . (p. 506)To transform the equation A x 2 +Bxy+C y 2 +Dx+Ey+F=0B0 into one in x and y without an xy-term , rotate the axes through an acute angle that satisfies the equation ________.Except for degenerate cases, the equation A x 2 +Bxy+C y 2 +Dx+Ey+F=0 defines a(n) _______ if B 2 4AC=0 . (a) circle (b) ellipse (c) hyperbola (d) parabolaExcept for degenerate cases, the equation A x 2 +Bxy+C y 2 +Dx+Ey+F=0 defines an ellipse if __________.8AYU9AYU10AYU11AYU12AYU13AYU14AYU15AYU16AYU17AYU18AYU19AYU20AYU21AYU22AYU23AYU24AYU25AYU26AYU27AYU28AYU29AYU30AYUIn Problems 31-42, rotate the axes so that the new equation contains no xy -term. Analyze and graph the new equation. Refer to Problems 21-30 for Problems 31-40. x 2 +4xy+ y 2 3=0In Problems 31-42, rotate the axes so that the new equation contains no xy -term. Analyze and graph the new equation. Refer to Problems 21-30 for Problems 31-40. x 2 4xy+ y 2 3=0In Problems 31-42, rotate the axes so that the new equation contains no xy -term. Analyze and graph the new equation. Refer to Problems 21-30 for Problems 31-40. 5 x 2 +6xy+5 y 2 8=0In Problems 31-42, rotate the axes so that the new equation contains no xy -term. Analyze and graph the new equation. Refer to Problems 21-30 for Problems 31-40. 3 x 2 10xy+3 y 2 32=035AYUIn Problems 31-42, rotate the axes so that the new equation contains no xy -term. Analyze and graph the new equation. Refer to Problems 21-30 for Problems 31-40. 11 x 2 10 3 xy+ y 2 4=0In Problems 31-42, rotate the axes so that the new equation contains no xy -term. Analyze and graph the new equation. Refer to Problems 21-30 for Problems 31-40. 4 x 2 4xy+ y 2 8 5 x16 5 y=0In Problems 31-42, rotate the axes so that the new equation contains no xy -term. Analyze and graph the new equation. Refer to Problems 21-30 for Problems 31-40. x 2 +4xy+4 y 2 +5 5 y+5=0In Problems 31-42, rotate the axes so that the new equation contains no xy -term. Analyze and graph the new equation. Refer to Problems 21-30 for Problems 31-40. 25 x 2 36xy+40 y 2 12 13 x8 13 y=0In Problems 31-42, rotate the axes so that the new equation contains no xy -term. Analyze and graph the new equation. Refer to Problems 21-30 for Problems 31-40. 34 x 2 24xy+41 y 2 25=0In Problems 31-42, rotate the axes so that the new equation contains no xy -term. Analyze and graph the new equation. Refer to Problems 21-30 for Problems 31-40. 16 x 2 +24xy+9 y 2 130x+90y=0In Problems 31-42, rotate the axes so that the new equation contains no xy -term. Analyze and graph the new equation. Refer to Problems 21-30 for Problems 31-40. 16 x 2 +24xy+9 y 2 60x+80y=043AYU44AYU45AYU46AYU47AYU48AYU49AYU50AYU51AYU52AYU53AYU54AYU55AYU56AYU57AYU58AYU59AYU60AYU1AYU2AYU3AYU4AYU5AYU6AYU7AYU8AYU9AYU10AYU11AYU12AYUIn Problems 13-24, analyze each equation and graph it. r= 1 1+cosIn Problems 13-24, analyze each equation and graph it. r= 3 1sinIn Problems 13-24, analyze each equation and graph it. r= 8 4+3sin16AYU17AYU18AYU19AYUIn Problems 13-24, analyze each equation and graph it. r= 8 2+4cos21AYU22AYU23AYU24AYU25AYU26AYU27AYU28AYU29AYU30AYU31AYU32AYU33AYU34AYU35AYU36AYU37AYU38AYU39AYU40AYU41AYU42AYU43AYU44AYU45AYU46AYUThe function f( x )=3sin( 4x ) has amplitude _______ and period _______. (pp. 412-414)2AYU3AYU4AYU5AYU6AYU