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JEE Main 2012Offline

Exam: JEE Main
Year: 2012
Mode: Offline
Subject: Mathematics
Chapter: Ellipse

JEE Main 2012 · Offline · Mathematics · Ellipse

An ellipse is drawn by taking a diameter of the circle...

An ellipse is drawn by taking a diameter of the circle

(x-1)^2+y^2=1

as its semiminor axis and a diameter of the circle

x^2+(y-2)^2=4

as its semi-major axis. If the centre of the ellipse is the origin and its axes are the coordinate axes, then the equation of the ellipse is

Options

A $4 x^2+y^2=4$
B $x^2+4 y^2=8$
C $4 x^2+y^2=8$
D $x^2+4 y^2=16$

Correct answer

D. $x^2+4 y^2=16$

Step-by-step solution

Semi minor axis

b=2

Semi major axis

a=4

Equation of ellipse

=\frac{x^2}{a^2}+\frac{y^2}{b^2}=1 \quad \Rightarrow \frac{x^2}{16}+\frac{y^2}{4}=1

\Rightarrow x^2+4 y^2=16

.

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