Question

Find the foci of the ellipse whose major axis has endpoints $(0,0)$ and $(13,0)$ and whose minor axis has length 12.

Answer 1

clearly the major axis has length 13, and the minor axis has length 12. So

a = 13/2
b = 6
c^2 = a^2-b^2 = 25/4, so c = 5/2

The center is at (13/2,0), so
h = 13/2 and k=0

The foci are at (h±c,k)

Since the major axis is horizontal, that means the equation is

(x-h)^2/a^2 + (y-k)^2/b^2 = 1
(x - 13/2)^2/(13/2)^2 + y^2/6^2 = 1

see

http://www.wolframalpha.com/input/?i=ellipse+%28x+-+13%2F2%29^2%2F%2813%2F2%29^2+%2B+y^2%2F6^2+%3D+1

Answer 2

tysm

Answer 3

Find the foci of the ellipse whose major axis has endpoints $(0,0)$ and $(13,0)$ and whose minor axis has length 12.

the answers are (9,0) and (4,0).