find the equation of the ellipse in the following cases:
Vertices (± 6, 0), foci (± 4, 0)
Given that we need to find the equation of the ellipse whose vertices are (±6,0) and foci (±4,0).
Let us assume the equation of the ellipse as (a2>b2).
We know that vertices of the ellipse are (±a,0)
⇒ a = 6
⇒ a2 = 36
We know that foci = (±ae,0)
⇒ ae = 4
⇒ 6e = 4
⇒
We know that eccentricity
⇒
⇒
⇒
⇒ b2 = 20
The equation of the ellipse is
⇒
⇒
⇒ 5x2 + 9y2 = 180
∴ The equation of the ellipse is 5x2 + 9y2 = 180.