Find the standard form of the equation of the ellipse: Foci: (0, 3), (0, -3) ; vertices: (0, -8), (0, 8)?

Answer 1

general equation, center at origin, is
x²/a² + y²/b² = 1. With vertices at ±8 on x axis, a = 8. c is distance center to focus, here 3, and c² = a² - b², so we have 9 = 64 - b², b² = 55. Thus the equation is
x²/64 + y²/55 = 1

Answer 2

(x^2)/(8^2) + (y^2)/(sqrt55)^2= 1