SOLUTION: An ellipse with center at the origin and the horizontal major axis is to fit snugly insidde a rectangle that has its longer sides horzontal. The area of the rectangle is 12 square

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Question 328087: An ellipse with center at the origin and the horizontal major axis is to fit snugly insidde a rectangle that has its longer sides horzontal. The area of the rectangle is 12 square units, and the perimeter is 14 units find an equation for the ellipse.
Answer by galactus(183) About Me  (Show Source):
You can put this solution on YOUR website!
The rectangle has perimeter 2x+2y=14
and area xy=12
Solve area for y and sub into perimeter, y=12/x
2x%2B2%2812%2Fx%29=14
x=4 or x=3
x is the longer one, so x=4 and y=3
This means the semi-major axis has length 2 and the semi-minor axis has length
3/2
So, the ellipse equation is x%5E2%2F%282%29%5E2%2By%5E2%2F%283%2F2%29%5E2=1

x%5E2%2F4%2B4y%5E2%2F9=1