The eccentricity of an ellipse, with its centre at the origin, is $\frac{1}{2}$. If one of the directrices…
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
$3 x^2+4 y^2=1$
$3 x^2+4 y^2=12$
$4 x^2+3 y^2=12$
$4 x^2+3 y^2=1$
Solution
Equation of directrix is $x=a / e=4 \Rightarrow a=2$
$
b^2=a^2\left(1-e^2\right) \Rightarrow b^2=3
$
Hence equation of ellipse is $3 x^2+4 y^2=12$