Solve the Problem $\frac { x ^ { 2 } } { 256 } + \frac { y ^ { 2 } } { 64 } = 1$

Solve the problem.
-A homeowner wants to make an elliptical rug from a 30-foot by 10-foot rectangular piece of carpeting.
a. What lengths of the major and minor axes would maximize the area of the new rug?
b. Write an equation of the ellipse with maximum area. Use a coordinate system with the origin at the center
Of the rug and horizontal major axis.

A) a. Major axis: 32 feet. Minor axis: 16 feet
b. $\frac { x ^ { 2 } } { 256 } + \frac { y ^ { 2 } } { 64 } = 1$
B) a. Major axis: 15 feet. Minor axis: 5 feet
b. $\frac { x ^ { 2 } } { 225 } + \frac { y ^ { 2 } } { 25 } = 1$
C) a. Major axis: 30 feet. Minor axis: 10 feet
b. $\frac { x ^ { 2 } } { 900 } + \frac { y ^ { 2 } } { 100 } = 1$
D) a. Major axis: 30 feet. Minor axis: 10 feet
b. $\frac { x ^ { 2 } } { 225 } + \frac { y ^ { 2 } } { 25 } = 1$