Find the standard form of the equation of each ellipse satisfying the given conditions?

Question

foci: (-5,0),(5,0),

vertices: (-8,0),(8,0)

Answer 1

ae = 5 and a = 8

b^2 = a^2(1 - e^2) = a^2 - a^2e^2

=> b^2 = (8)^2  - (5)^2 = 39

The standard equation of the ellipse is

x^2/a^2 + y^2/b^2 = 1

=> x^2/64 + y^2/39 = 1