Asked by marlene

Hi,
i would like to know how would i write a standard form equation of each ellipse

vertices : (-6,18),(-6,-8)
foci: (-6,5+ sq root 165),(-6,5-sq root 165)
Answered by Steve
center is at (-6,5) so

(x+6)^2/a^2 + (y-5)^2/b^2 = 1

The semi-major axis is vertical,and of length 13.

c^2 = a^2-b^2
165 = 169-4, so b=2

(x+6)^2/4 + (y-5)^2/169 = 1

see

http://www.wolframalpha.com/input/?i=ellipse+%28x%2B6%29^2%2F4+%2B+%28y-5%29^2%2F169+%3D+1
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