Question

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

• A. $4x^2+3y^2=1$
• B. $3x^2+4y^2=12$
• C. $4x^2+3y^2=12$
• D. $3x^2+4y^2=1$

Answer 1

The correct option is B $3x^2+4y^2=12$

Given, $e=\frac{1}{2}$, Directrix, $x=\frac{a}{e}=4$

Therefore, $a=4\times \frac{1}{2}=2$

Thus $b=2\sqrt{1-\frac{1}{4}}=\sqrt{3}$

Equation of ellipse is $\frac{x^2}{4}+\frac{y^2}{3}=1$

$\Rightarrow 3x^2+4y^2=12$