find the equation of the ellipse in the following cases:
Vertices (0, ±13), foci (±4, 0)

Question

find the equation of the ellipse in the following cases:Vertices (0, ±13), foci (±4, 0)

Philoid · Accepted Answer

Given that we need to find the equation of the ellipse whose vertices are (0,±13) and foci (±4,0).

Let us assume the equation of the ellipse as (a²>b²).

We know that vertices of the ellipse are (0,±b)

⇒ b = 13

⇒ b² = 169

We know that foci = (±ae,0)

⇒ ae = 4

We know that eccentricity

⇒

⇒ 16 = a² - 169

⇒ a² = 185

The equation of the ellipse is

⇒

∴ The equation of the ellipse is .