Question

Find an equation for the ellipse that satisfies the given conditions.

eccentricity = 1/3
foci = (0, +-7)

I thought it would be x^2/392 + y^2/348 = 1 but I've tried several times and keep getting different answers...any help would be appreciated! Thanks :)

Answer 1

\[
\frac 7 a=e=\frac 1 3\implies a=21
\]

Answer 2

\[
b^2=a^2-c^2= 21^2 -7^2=392
\]

Answer 3

\[
a^2=21^2=441
\]

Answer 4

\[
\frac {x^2}{441}+\frac {y^2}{392}=1
\]

Answer 5

Thank you so much! :) @eliesaab

Answer 6

YW