Question

$PSQ$ is a focal chord of the ellipse $\frac{x^2}{4}+\frac{y^2}{9}=1$, then $\frac{1}{SP}+\frac{1}{SQ}=$

• A. $\frac{2}{3}$
• B. $\frac{3}{2}$
• C. $\frac{4}{3}$
• D. $\frac{4}{9}$

Answer 1

The correct option is B $\frac{3}{2}$

$\frac{x^2}{4}+\frac{y^2}{9}=1$, Comparing with $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$

$a=2,b=3(b>a)$

Therefore, $SP=\frac{a^2}{b}=\frac{4}{3}=SQ$

Now, $\frac{1}{S.P}+\frac{1}{S.Q}=\frac{1}{\frac{4}{3}}+\frac{1}{\frac{4}{3}}=\frac{3}{4}+\frac{3}{4}=\frac{3}{2}$