EllipseHardBloom L3
Question
If $S$ and $S^{'}$ are the foci of the ellipse $\frac{x^{2}}{25} + \frac{y^{2}}{16} = 1$ and $P$ is any point on it, then difference of maximum and minimum of $SP.S^{'}P$ is equal to:
Options
A.16
B.9
C.15
D.25
Solution
Sol.(b) $(SP)\left( S^{'}P \right) = a(1 - ecos\theta)a(1 + ecos\theta)$
$$\begin{matrix} & \ = a^{2} - a^{2}e^{2}\cos^{2}\theta \\ & \ = 25 - 9\cos^{2}\theta \\ & \ max = 25 - 9(0) = 25 \\ & \ min = 25 - 9(1) = 16 \\ & \ max - min = 25 - 16 = 9 \end{matrix}$$
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