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 $S{S}^{\prime }=$

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

Answer 1

The correct option is A $4+S^{\prime }P$

$S{S}^{\prime }=2ae=2\times a\times \sqrt{1-\frac{b^2}{a^2}}$

$S{S}^{\prime }=2\times 5\times \frac{3}{5}=6\dots \left(1\right)$

As we know $SP+S^{\prime }P=2a=10$

$\Rightarrow S^{\prime }P=10-SP=10-8=2\Rightarrow S^{\prime }P=2$

From equation (1)

$S{S}^{\prime }=6=4+S^{\prime }P$