Question

Equation of the ellipse whose foci are $(\pm 2,0)$ and eccentricity is $\frac{1}{2}$ is

• A. $\frac{x^2}{12}+\frac{y^2}{16}=1$
• B. $\frac{x^2}{16}+\frac{y^2}{12}=1$
• C. $\frac{x^2}{16}+\frac{y^2}{8}=1$
• D. $\frac{x^2}{16}+\frac{y^2}{8}=-1$

Answer 1

The correct option is B $\frac{x^2}{16}+\frac{y^2}{12}=1$

Given, eccentricity $e=\frac{1}{2}$

$\therefore a\times \frac{1}{2}=2$
$\therefore a=4$
We know, $e^2=\frac{a^2-b^2}{a^2}$
$\frac{1}{4}=1-\frac{b^2}{4^2}$
$b^2=12$
$\frac{x^2}{16}+\frac{y^2}{12}=1$