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JEE Main 201912 AprilEvening Shift

Exam: JEE Main
Year: 2019
Date: 12 April
Shift: Evening Shift
Subject: Mathematics
Chapter: Ellipse

JEE Main 2019 · 12 April · Evening Shift · Mathematics · Ellipse

An ellipse, with foci at (0,2) and (0, - 2) and minor axis of...

An ellipse, with foci at

\left(0,2\right)

and

\left(0, - 2\right)

and minor axis of length

4

, passes through which of the following points?

Options

A $\left(1, 2\sqrt{2}\right)$
B $\left(2, \sqrt{2}\right)$
C $\left(\sqrt{2}, 2\right)$
D $\left(2, 2\sqrt{2}\right)$

Correct answer

C. $\left(\sqrt{2}, 2\right)$

Step-by-step solution

Given that be

= 2 and

a = 2

<br/>(here

a < b

) <br/>

∵ {a}^{2} = {b}^{2}\left(1 - {e}^{2}\right)

<br/>

∴ {b}^{2} = 8

<br/>

∴

Equation of ellipse

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

<br/>Clearly \left(\sqrt{2}, 2\right)

lies on the ellipse.

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