Question

If two foci of an ellipse be $(-2,0)$ and $(2,0)$ and its eccentricity is $\frac{2}{3}$ then the ellipse has the equation

• A. $5x^2+9y^2=45$
• B. $9x^2+5y^2=45$
• C. $5x^2+9y^2=90$
• D. $9x^2+5y^2=90$

Answer 1

The correct option is A $5x^2+9y^2=45$

Given focii are $(-2,0)$ and $(2,0)$
$\Rightarrow$ centre of the ellipse $\equiv C(0,0)$
Also $ae=2$ and $e=\frac{2}{3}$
$\Rightarrow a=3,b^2=a^2(1-e^2)=5$
Therefore required ellipse is, $\frac{x^2}{9}+\frac{y^2}{5}=1$
$\Rightarrow 5x^2+9y^2=45$