Q. A point $P$ moves so that sum of its distances from $(–ae,0)$ and $(ae,0)$ is $2a$. Then, the locus of $P$ is
A) $\frac{x^{2}}{a^{2}} - \frac{x^{2}}{a^{2}\left( 1 - e^{2} \right)} = 1$
B) $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{a^{2}\left( 1 - e^{2} \right)} = 1$
C) $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{a^{2}\left( 1 + e^{2} \right)} = 1$
D) $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{a^{2}\left( 1 + e^{2} \right)} = 1$
Explanation
(d)
Let the equation of ellipse be
$\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$
$\because\ b^{2} = a^{2}\left( 1 - e^{2} \right)$
$\therefore\ \frac{x^{2}}{a^{2}} + \frac{y^{2}}{a^{2}(1 - e^{2})} = 1$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.