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