Write an equation of the ellipse with foci at (0, ±3) and co-vertices at (±3, 0).

Question

whats the equation of the ellipse with foci at (0, ±3) and co-vertices at (±3, 0).

Answer 1

The co-vertices being (±3,0) means the semi-minor axis is 3 = b < a, the semi-major axis in x²/b² + y²/a² = 1, unlike the usual formula. The foci being at (0,±3) means the linear eccentricity is 3 = c = √(a² – b²), so a = √(c² + b²) = √18 so the equation is x²/9 + y²/18 = 1,