SOLUTION: find an equation of the ellipse that has a center (2,5), a major axis of length 12, and endpoint of minor axis (2,3)

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Question 1201708: find an equation of the ellipse that has a center (2,5), a major axis of length 12, and endpoint of minor axis (2,3)
Answer by greenestamps(13209) About Me  (Show Source):
You can put this solution on YOUR website!


Center (2,5) and one end of minor axis (2,3) means the minor axis is vertical, so the general equation is

%28x-h%29%5E2%2Fa%5E2%2B%28y-k%29%5E2%2Fb%5E2=1

The center is (h,k); a is the semi-major axis; b is the semi-minor axis.

The center (h,k) is given.
The length of the major axis is 12, so a = 6.
The length of the semi-minor axis, b, is the distance from (2,5) to (2,3), which is 2.

So

%28x-2%29%5E2%2F6%5E2%2B%28y-5%29%5E2%2F2%5E2=1

ANSWER: %28x-2%29%5E2%2F36%2B%28y-5%29%5E2%2F4=1