Question

Write an equation for the ellipse that satisfies the set of conditions.

endpoint of major axis at ( 0, 10) and (0, -10) foci at (0, 8) and (0-8)

Please help, I really don't understand how to do this

Answer 1

an ellipse with center at (h,k) and semi-axes a and b is

(x-h)^2/a^2 + (y-k)^2/b^2 = 1
the foci are at c where a^2 = b^2 + c^2 and lie on the major axis.

you thus have

a = 10
c = 8
so, b = 6

It appears that the center is at (0,0), so

x^2/100 + y^2/36 = 1