An ellipse, with foci at (0, 2) and (0, -2) and minor axis of length 4, passes through which of the following points?

Correct option is D (2,2)
Step 1: Find length of major axis using formula of eccentricity
Given that foci of the ellipse is at (0,2) (0,−2); ⇒Major axis of ellipse is along y-axis.
So, equation of ellipse can be taken as x²/a² + y²/b² = 1, where, a<b
Length of minor axis, 2a=4 (Given) ⇒a=2
be=2 ( ∵ e=√(1−a²/b²) ⇒a²=b²−b² ⇒4=b²−4 (From eq. (1) (2))
⇒b²=8 ⇒b=2√2
(Step 2: Find equation of ellipse using above result
Using eq (1) (3), we have equation of ellipse is as follows:
x²/4 + y²/8 = 1
Checking options, we have (2,2) satisfying the equation of ellipse above.
Hence, (D) is the correct option.