An ellipse, with foci at (0,2) and (0,–2) and minor axis of length 4 units, passes through which of the following points?
A
(2,√2)
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B
(1,2√2)
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C
(√2,2)
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D
(2,2√2)
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Solution
The correct option is C(√2,2) Foci are (0,2) and (0,–2) So, major axis is y-axis. Let the equation of ellipse be x2a2+y2b2=1(b>a)
Given, 2a=4 and 2be=4 ⇒a=2,be=2 ⇒b2e2=4⇒b2−a2=4⇒b2=8 Therefore, equation of the ellipse is x24+y28=1 By putting all the points, we get that (√2,2) lies on the ellipse.