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, e = $\sqrt{1-\frac{4}{9}}$ = $\frac{\sqrt{5}}{3}$, Length of the lactus rectum = $\frac{2a^2}{b}$ = $\frac{2\times 4}{3}$ = $\frac{8}{3}$

$\frac{1}{SP}+\frac{1}{SQ}$ = $\frac{2}{l}$ = $\frac{3}{2}$