find the equation of the ellipse in the following cases:
eccentricity and foci (± 2, 0)
Given that we need to find the equation of the ellipse whose eccentricity is and foci (±2,0).
Let us assume the equation of the ellipse as (a2>b2).
We know that eccentricity(e) =
⇒
⇒
⇒
⇒
We know that foci = (±ae,0)
⇒ ae = 2
⇒
⇒ a = 4
⇒ a2 = 16
⇒
⇒ b2 = 12
The equation of the ellipse is
⇒
⇒
⇒ 3x2 + 4y2 = 48
∴ The equation of the ellipse is 3x2 + 4y2 = 48.