Find an equation for the ellipse that has its center at the origin and satisfies the given conditions. vertices V(0, ±6), passing through (4, 3)

Question

Find an equation for the ellipse that has its center at the origin and satisfies the given conditions.

vertices V(0, ±6),    passing through (4, 3)

Answer 1

An ellipse centered at the origin is defined by x^2/a^2 + y^2/b^2 = 1

As there is a vertex at (0, 6), b = 6

As it passes through (4, 3), then, 4^2/a^2 + 3^2/6^2 = 1

4^2/a^2 = 3/4

3a^2 = 64

a^2 = 64/3

The ellipse is defined as

3x^2/64 + y^2/36 = 1