Question

If $S$ and $S^{{}^{\prime }}$ are the foci of the ellipse $\frac{x^2}{25}+\frac{y^2}{16}=1$ and if $PS{P}^{{}^{\prime }}$ is a focal chord with $SP=8$, then $S{S}^{\prime }$ is equal to

• A. $4+S^{{}^{\prime }}P$
• B. $S^{{}^{\prime }}P-1$
• C. $4+SP$
• D. $SP-1$

Answer 1

Answer: (A)

Given equation of ellipse
$\frac{x^2}{25}+\frac{y^2}{16}=1$
Here, $a=5$ and $b=4$
$e=\sqrt{1-\frac{b^2}{a^2}}=\sqrt{1-\frac{16}{25}}$
$=\sqrt{\frac{9}{25}}=\frac{3}{5}$

Also,$PS+P{S}^{{}^{\prime }}=2a=2\times 5=10$
$\Rightarrow P{S}^{{}^{\prime }}=10-8[\because SP=8]$
$\Rightarrow P{S}^{{}^{\prime }}=2$
Now, $S{S}^{{}^{\prime }}=2ae=2\times 5\times \frac{3}{5}=6$
From options, $S{S}^{{}^{\prime }}=4+S^{{}^{\prime }}P$