Question

Need some help.
Find the standard equation for of the elipse centered at the origin with foci at (0,8), (0,-8) and eccentricity e-.2

so far I have c=8 and a =40 and b =16*sqrt(6) but when i build the equation it doesnt come out

Answer 1

Okay.
So the major axis of the ellipse is on the y-axis and the minor axis is on the x-axis. So the formula: \[b^2=a^2(1-e^2)\]
becomes
\[a^2=b^2(1-e^2)\]

Answer 2

This is what I came up with
\[ e=c/a →e=1/5 →c=±8 →e=8/40 →a=40 →b=√(〖40〗^2-8^2 )=16√6 →x^2/(16√6)^2 +y^2/〖40〗^2 =1 \]

Answer 3

=16√6 →x^2/(16√6)^2 +y^2/〖40〗^2 =1