Question

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

(A) $\frac{x^2}{3}+\frac{y^2}{4}=1$

(B) $\frac{x^2}{4}+\frac{y^2}{3}=1$

(C) $\frac{x^2}{4}+\frac{y^2}{3}=\frac{4}{3}$

(D) None of these

Answer 1

SOLUTION — Here,

$e=\frac{1}{2} \text { and } a e= \pm 1 \Rightarrow a= \pm 2$

$\begin{array}{ll}\therefore b^2=a^2\left(1-e^2\right)=4\left(1-\frac{1}{4}\right)=3 \\\therefore \text { Equation is } \frac{x^2}{4}+\frac{y^2}{3}=1\end{array}$

So, The correct option will be (B).