Question

If $F_1,F_2$ be the feet of the perpendiculars from the foci $S_1,S_2$ of an ellipse $\frac{x^2}{5}+\frac{y^2}{3}=1$ on the tangent at any point P on the ellipse then $S_1{F}_1.S_2{F}_2=$

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

The product of the perpendiculars from the foci onto a tangent to the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1(a>b)$ is $b^2$
$\therefore$ $S_1{F}_1.S_2{F}_2=b^2=3$