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10-2. Parabola, Ellipse, Hyperbola
normal
If $F_1$ and $F_2$ be the feet of the perpendicular from the foci $S_1$ and $S_2$ of an ellipse $\frac{{{x^2}}}{5} + \frac{{{y^2}}}{3} = 1$ on the tangent at any point $P$ on the ellipse, then $(S_1 F_1) (S_2 F_2)$ is equal to
A
$2$
B
$3$
C
$4$
D
$5$
Solution
We know that the product of perpendiculars from two foci of an ellipse upon any tangent is equal to the square of the semi-minor axis.
$\left(S_{1} F_{1}\right)\left(S_{2} F_{2}\right)=3$
Standard 11
Mathematics
