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. $\frac{x^2}{3}+\frac{y^2}{4}=\frac{4}{3}$
• D. None of these

Answer 1

Answer: (B)

Given that, $e=\frac{1}{2}$ and $(\pm ae,0)=(\pm 1,0)$
$\Rightarrow ae=1\Rightarrow a=2$
Now, $b^2=a^2\left(1-e^2\right)$
$\Rightarrow b^2=4\left(1-\frac{1}{4}\right)\Rightarrow b^2=3$
Hence, equation of ellipse is $\frac{x^2}{4}+\frac{y^2}{3}=1$.