find the equation of the ellipse in the following cases:
Ends of the major axis (± 3, 0), and of the minor axis (0, ±2)
Given that we need to find the equation of the ellipse whose ends of the major axis is (±3,0) and ends of the minor axis is (0,±2).
Let us assume the equation of the ellipse as (a2>b2).
We know that ends of the major axis of the ellipse are (±a,0)
⇒ a = 3
⇒ a2 = 9
We know that ends of minor axis of the ellipse are (0,±b)
⇒ b = 2
⇒ b2 = 4
The equation of the ellipse is
⇒
⇒
⇒ 4x2 + 9y2 = 36
∴ The equation of the ellipse is 4x2 + 9y2 = 36.