find the equation of the ellipse in the following cases:
Ends of the major axis (0, ± ), ends of the minor axis (±1,0)
Given that we need to find the equation of the ellipse whose ends of major axis are and ends of the minor axis are (±1,0).
Let us assume the equation of the ellipse as (b2>a2).
We know that ends of the major axis of the ellipse are (0,±b)
⇒
⇒ b2 = 5
We know that ends of the minor axis of the ellipse are (±a,0)
⇒ a = 1
⇒ a2 = 1
The equation of the ellipse is
⇒
⇒
⇒ 5x2 + y2 = 5
∴ The equation of the ellipse is 5x2 + y2 = 5.