Q. The equation of the ellipse whose foci are $( \pm 2,0)$ and eccentricity $\frac{1}{2}$ is
A) $\frac{x^{2}}{12} + \frac{y^{2}}{16} = 1$
B) $\frac{x^{2}}{16} + \frac{y^{2}}{12} = 1$
C) $\frac{x^{2}}{16} + \frac{y^{2}}{8} = 1$
D) None of these
Explanation
(b)
It is given that $e = \frac{1}{2}ae = 2$
Therefore, $a = 4$
$\because b^{2} = a^{2}\left( 1 - e^{2} \right)$
$\Rightarrow \ b^{2} = 12$
Thus, the required ellipse is $\frac{x^{2}}{16} + \frac{y^{2}}{12} = 1$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.