Use the method of Lagrange multipliers to find the dimensions of the rectangle 1 with sides parallel to the coordinate 2 2 x²y² + 9 4 of greatest area that can be inscribed in the ellipse axes. 3 -2 -1 15 1 0 -1. 2 1 2 B

Q: The parabola y = ² is changed to the form y = a (x − p)² + g by translating the parabola 2 units…

A: The parabola y=x2 is changed to the form y=ax-p2+q by translating the parabola 2 units down and 3…

Q: Use the method of Lagrange Multipliers to find the area of the largest rectangle with edges parallel…

A: The rectangle inscribed the ellipse x218+y232=1. Let sides of rectangle be 2x and  2y.  Draw the…

Q: find the coordinates of the vertex and the focus for the parabola given by x2+6x+24y-111=0

A: SOLUTION-

Q: A rectangle is inscribed in the first quadrant region bounded by the r-axis, the y-axis, and the…

A: Let the two lower vertex of the rectangle be (x,0) and (−x,0). That implies, the length of the base…

Q: Identify the quadratic surface of the equation 6x? + 3y? + 222 + 24x – 6y – 12z + 39 = 0 Choose an…

A: Given, 6x ^ 2 + 3y ^ 2 + 2z ^ 2 + 24x - 6y - 12z + 39 = 0

Q: Complete the square method: Show all your work! Put x² + y² 10x + 6y 15 = 0 in center radius form.…

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Q: A craftsman wants to draw a leaf repetitively on some vases. He wants to know the area covered by…

A:

Q: Show, by completing the square, that the parabolay = ax2 + bx +c can be obtained from y = ax 2 by a…

A: The given equation of parabola is y=ax2+bx+c. Rewrite the above equation as follows.…

Q: Find the points of intersection between the line 4y - 3x + 12 = 0 and the ellipse 9x 2 + 16y 2 =…

A: The line 4y-3x+12=0 And the Ellipse 9x2+16y2=144 We need to find the intersection point of the line…

Q: Express the general form to its standard form and locate the center, vertices, covertices and foci…

A: equation 4x2 - y2 - 32x - 4y + 24 = 0

Q: Which parabola has a vertex at the (0, 3) and opens to the right? Oy=x²+3 y = -(x + 3)² Ox=y²-3 O x…

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Q: parabola passes through (15,0) (25,30) (35,80). find the equation of the parabola in the form…

A: Given: A parabola passes through (15,0) (25,30) (35,80). To find:- The equation of the parabola in…

Q: Find the area of the largest rectangle that can be inscribed in the ellipse  x2/a2 + y2/b2 = 1.

A: Let (x,y) be a vertex of rectangle. Then, length of rectangle = 2x, width = 2y. Then area of…

Q: Find the point on the ellipse x² + 6y² + 3xy = 40 with the greatest x-coordinate. (Use decimal…

A: We have to find the point on the ellipsex2+6y2+3xy = 40With the greatest x-coordinate.For this we…

Q: Find an equation of the sphere whose diameter is the line segment having endpoints at (6,2, –5)

A: To find the equation of sphere.