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A company constructs rectangular seating plans and arranges seats for pop concerts on AFL grounds. All AFL grounds used are elliptical in shape and the equation of the ellipse illustrated a2 y? y4 A(x, y) seating is a2 = 1 where a and b are the lengths 62 of its semi-major and semi-minor axes as shown. -stage a Show that y = -Va² – x² _for A as shown. a 6 Show that the seating area is given 4bx A(x) = a c Show that A'(x) = 0 when x = a d Prove that the seating area is a maximum when e Given that the area of the ellipse is rab, what percentage of the ground is occupied by the seats in the optimum case?

A company constructs rectangular seating plans and arranges seats for pop concerts on AFL grounds. All AFL grounds used are elliptical in shape and the equation of the ellipse illustrated a2 y? y4 A(x, y) seating is a2 = 1 where a and b are the lengths 62 of its semi-major and semi-minor axes as shown. -stage a Show that y = -Va² – x² _for A as shown. a 6 Show that the seating area is given 4bx A(x) = a c Show that A'(x) = 0 when x = a d Prove that the seating area is a maximum when e Given that the area of the ellipse is rab, what percentage of the ground is occupied by the seats in the optimum case?

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter7: Conic Sections And Quadratic Systems
Section7.2: The Ellipse
Problem 69E
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i need help with parts d and e only, with work. thank you.
A company constructs rectangular seating plans and arranges seats for pop concerts on AFL grounds. All AFL grounds used are elliptical in yA A(x, y) shape and the equation of the ellipse illustrated seating x2 is a2 y? = 1 where a and b are the lengths 62 of its semi-major and semi-minor axes as shown. -stage a Show that y= b a² – x² _for A as shown. а 4bx 6 Show that the seating area is given by A(x) = a а c Show that A'(x) = 0 when x = a d Prove that the seating area is a maximum when x = e Given that the area of the ellipse is rab, what percentage of the ground is occupied by the seats in the optimum case?
Transcribed Image Text:A company constructs rectangular seating plans and arranges seats for pop concerts on AFL grounds. All AFL grounds used are elliptical in yA A(x, y) shape and the equation of the ellipse illustrated seating x2 is a2 y? = 1 where a and b are the lengths 62 of its semi-major and semi-minor axes as shown. -stage a Show that y= b a² – x² _for A as shown. а 4bx 6 Show that the seating area is given by A(x) = a а c Show that A'(x) = 0 when x = a d Prove that the seating area is a maximum when x = e Given that the area of the ellipse is rab, what percentage of the ground is occupied by the seats in the optimum case?
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