Q. Let $P$ be a variable point on the ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$, with foci $S_{1}$ and $S_{2}$, then coordinates of $P$ such that area of $\mathrm{\Delta}S_{1}\ {PS}_{2}$ is maximum, are
A) $(0,\ b)$
B) $\left( \frac{a}{2},\ \frac{\sqrt{3}}{2}b \right)$
C) $\left( \frac{\sqrt{3}}{2}a,\ \frac{b}{2} \right)$
D) None of these
Explanation
(a)
To maximise the area of $\mathrm{\Delta}S_{1}{PS}_{2}$ altitude should be maximum as base $S_{1},\ S_{2}$ is fixed. So, $P$ should be $(0,\ b)$
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Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.