SOLUTION: Find the equation of the ellipse with foci at (-4,0) and (-4,6) and vertex at (-4,8)

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Question 1026558: Find the equation of the ellipse with foci at (-4,0) and (-4,6) and vertex at (-4,8)
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
The major axis of the ellipse is parallel to the y-axis, and as such would take on the standard form %28x-h%29%5E2%2Fb%5E2%2B%28y-k%29%5E2%2Fa%5E2+=+1.
The center of the ellipse is easy enough--it should be the point (-4,3).
Now for the ellipse, b%5E2%2Bc%5E2+=a%5E2.
a = distance from the center to a vertex, hence a = 5.
c = distance from the center to a focus, hence c = 3.
==> b%5E2%2B3%5E2=+5%5E2 ==> b%5E2+=+25-9+=+16
==> the equation of the ellipse is %28x%2B4%29%5E2%2F16%2B%28y-3%29%5E2%2F25+=+1.