Question

If $S$ and $S^{\prime }$ are the foci of the ellipse $\frac{x^2}{25}+\frac{y^2}{16}=1$, and $P$ is any point on it, then the range of values of $SP\cdot S^{\prime }P$ is

• A. $9\ge f\left(\theta \right)\ge 16$
• B. $9\ge f\left(\theta \right)\ge 25$
• C. $16\ge f\left(\theta \right)\ge 25$
• D. $1\ge f\left(\theta \right)\ge 16$

Answer 1

The correct option is A $9\ge f\left(\theta \right)\ge 16$

$\frac{x^2}{25}+\frac{y^2}{16}=1$

$\frac{1}{SP}+\frac{1}{SQ}=\frac{2a}{b^2}\Rightarrow \frac{1}{SP}+\frac{1}{SQ}=\frac{2\left(5\right)}{16}=\frac{5}{8}$

$SP+SQ=2a$

$=2\left(5\right)=10$