Write the equation for the ellipse centered at the origin with x -intercepts at 17 and −17 and foci located at (8,0) and (−8,0).

Answer 1

Standard form is (x-h)^2/a^2 + (y-k)^2/b^2 = 1. We need values of h, k, a, b

a = 17 = semi-major axis

Use c^2 = a^2 - b^2 to find b.

c = 8, a = 17. Solve 64 = 289 - b^2.

b = 15

Center is origin. So

h = 0, k = 0

Plug these values if a, b, h, k in the standard form.