SOLUTION: Find an equation for the ellipse satisfying the given conditions: Ends of major axis (±6,0); passes through (2,3).

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Question 769733: Find an equation for the ellipse satisfying the given conditions:
Ends of major axis (±6,0); passes through (2,3).
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Find an equation for the ellipse satisfying the given conditions:
Ends of major axis (±6,0); passes through (2,3).
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Given ellipse has a horizontal major axis.
Its standard form of equation: %28x-h%29%5E2%2Fa%5E2%2B%28y-k%29%5E2%2Fb%5E2=1, a>b, (h,k)=(x,y) coordinates of the center
center: (0,0)
a=6 (distance from center to vertices)
a^2=36
solving for b using coordinates of given point (2,3)
x%5E2%2F36%2By%5E2%2Fb%5E2=1
2%5E2%2F36%2B3%5E2%2Fb%5E2=1
4%2F36%2B9%2Fb%5E2=1
9/b^2=1-1/9=8/9
b^2/9=9/8
b^2=81/8
Equation:x%5E2%2F36%2B8y%5E2%2F81=1