Question

The eccentricity of an ellipse, with its centre at the origin, is $\frac{1}{2}$. If the equation of one of its directrices is x = 4, then the equation of the ellipse is

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

Centre = (0, 0), directrix $=4\Rightarrow \frac{a}{e}=4\Rightarrow a=2$
$b^2=a^2(1-e^2)=4(1-\frac{1}{4})=3$
Equation of the ellipse is $\frac{x^2}{4}+\frac{y^2}{3}=1\Rightarrow 3x^2+4y^2=12$