An ellipse, with foci at (0,2) and (0,–2) and minor axis of length 4, 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 x2b2+y2a2=1
Given, 2b=4 and 2c=4 ⇒b=2,c=2 ⇒c2=4⇒a2−b2=4⇒a2=8
Therefore, equation of the ellipse is x24+y28=1
By putting all the points, we get that (√2,2) lies on the ellipse.