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

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10-2. Parabola, Ellipse, Hyperbola

hard

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

A

$(2, \sqrt 2 )$

B

$(2, 2\sqrt 2 )$

C

$(1, 2\sqrt 2 )$

D

$( \sqrt 2, 2 )$

(JEE MAIN-2019)

Solution

Given $2a = 4$ and $2be = 4$

$ \Rightarrow a = 2,be = 2$

$ \Rightarrow {b^2}{e^2} = 4$

$ \Rightarrow {b^2} – {a^2} = 4$

$ \Rightarrow {b^2} = 8$

$ \Rightarrow $ equation of ellipse

$\frac{{{x^2}}}{4} + \frac{{{y^2}}}{8} = 1$

Clearly option $(D)$ satisfy the given curve.

Standard 11

Mathematics

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