For Exercises 49-51, an equation of a conic section (nondegenerative case) is given. a. Identify the type of conic section. b. Determine an acute angle of rotation to eliminate the x y term. c. Use a rotation of axes to eliminate the x y term in the equation. d. Sketch the graph. 47 x 2 + 34 3 x y + 13 y 2 − 64 = 0
For Exercises 49-51, an equation of a conic section (nondegenerative case) is given. a. Identify the type of conic section. b. Determine an acute angle of rotation to eliminate the x y term. c. Use a rotation of axes to eliminate the x y term in the equation. d. Sketch the graph. 47 x 2 + 34 3 x y + 13 y 2 − 64 = 0
Solution Summary: The author explains that the conic section is an equation of a hyperbola.
For Exercises 49-51, an equation of a conic section (nondegenerative case) is given.
a. Identify the type of conic section.
b. Determine an acute angle of rotation to eliminate the
x
y
term.
c. Use a rotation of axes to eliminate the
x
y
term in the equation.
d. Sketch the graph.
47
x
2
+
34
3
x
y
+
13
y
2
−
64
=
0
Curve that is obtained by the intersection of the surface of a cone with a plane. The three types of conic sections are parabolas, ellipses, and hyperbolas. The main features of conic sections are focus, eccentricity, and directrix. The other parameters are principal axis, linear eccentricity, latus rectum, focal parameter, and major and minor axis.
Points z1 and z2 are shown on the graph.z1 is at (4 real,6 imaginary), z2 is at (-5 real, 2 imaginary)Part A: Identify the points in standard form and find the distance between them.Part B: Give the complex conjugate of z2 and explain how to find it geometrically.Part C: Find z2 − z1 geometrically and explain your steps.
A polar curve is represented by the equation r1 = 7 + 4cos θ.Part A: What type of limaçon is this curve? Justify your answer using the constants in the equation.Part B: Is the curve symmetrical to the polar axis or the line θ = pi/2 Justify your answer algebraically.Part C: What are the two main differences between the graphs of r1 = 7 + 4cos θ and r2 = 4 + 4cos θ?
A curve, described by x2 + y2 + 8x = 0, has a point A at (−4, 4) on the curve.Part A: What are the polar coordinates of A? Give an exact answer.Part B: What is the polar form of the equation? What type of polar curve is this?Part C: What is the directed distance when Ø = 5pi/6 Give an exact answer.
Elementary Statistics: Picturing the World (7th Edition)
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