The eccentricity of an ellipse, with its centre at the origin, is 12.

Question

The eccentricity of an ellipse, with its centre at the origin, is $	frac12$. If one of the directrices is $x=4$, then the equation of the ellipse is:

Accepted Answer

Directrix $x=\dfrac ae=4\Rightarrow a=4\cdot	frac12=2$. $b^2=a^2(1-e^2)=4\left(1-	frac14ight)=3$.

Equation: $\dfrac{x^2}{4}+\dfrac{y^2}{3}=1\Rightarrow3x^2+4y^2=12.$

Solutions · 1