Question

Equation of the ellipse with centre at origin, passing through the point $(-3,1)$ and $e=\sqrt{\frac{2}{5}}$ is :

• A. $3x^2+5y^2=32$
• B. $3x^2+7y^2=34$
• C. $5x^2+3y^2=32$
• D. $3x^2+7y^2=36$

Answer 1

Answer: (A)

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

Let equation of ellipse be $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$

Since $e=\sqrt{\frac{2}{5}};b^2=a^2(1-e^2)$

$=a^2\left(\frac{3}{5}\right)$

Thus $\frac{x^2}{a^2}+\frac{5y^2}{3a^2}=1$

Since it passes through $(-3,1)$

$\Rightarrow \frac{9}{a^2}+\frac{5}{3a^2}=1$

$\Rightarrow \frac{32}{3a^2}=1$

$\Rightarrow a^2=\frac{32}{3}$

The equation of ellipse is $\frac{x^2}{\frac{32}{3}}+\frac{5y^2}{3\left(\frac{32}{3}\right)}=1$

$\Rightarrow 3x^2+5y^2=32$