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JEE Main 2011

Exam: JEE Main
Year: 2011
Subject: Mathematics
Chapter: Ellipse

JEE Main 2011 · Mathematics · Ellipse

Equation of the ellipse whose axes are the axes of coordinates and...

Equation of the ellipse whose axes are the axes of coordinates and which passes through the point

(-3,1)

and has eccentricity

\sqrt{\frac{2}{5}}

is

Options

A $5 x^2+3 y^2-48=0$
B $3 x^2+5 y^2-15=0$
C $5 x^2+3 y^2-32=0$
D $3 x^2+5 y^2-32=0$

Correct answer

D. $3 x^2+5 y^2-32=0$

Step-by-step solution

\begin{aligned}& \mathrm{b}^2=\mathrm{a}^2\left(1-\mathrm{e}^2\right)=\mathrm{a}^2\left(1-\frac{2}{5}\right)=\mathrm{a}^2 \frac{3}{5}=\frac{3 \mathrm{a}^2}{5}\\ & \frac{\mathrm{x}^2}{\mathrm{a}^2}+\frac{\mathrm{y}^2}{\mathrm{~b}^2}=1 \Rightarrow \frac{9}{\mathrm{a}^2}+\frac{5}{3 \mathrm{a}^2}=1 \\ & \mathrm{a}^2=\frac{32}{3}\\ & \mathrm{~b}^2=\frac{32}{5} \end{aligned}

\therefore

Required equation of ellipse

3 x^2+5 y^2-32=0$

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