Let equation of an ellipse is
$\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$... (i)
Its foci are $S(a e, 0)$ and $S'(-a e, 0)$. The equation of tangent at any point $(a \cos \theta, b \sin \theta)$ to ellipse is
$\frac{x}{a} \cos \theta+\frac{y}{b} \sin \theta=1$ ...(ii)
Let the perpendicular from $S$ and $S'$ upon Eq. (ii) be $SM$ and $S' N$.
Then, $S M \cdot S'N=\frac{-1}{\frac{\cos ^{2} \theta}{a^{2}}+ \frac{\sin ^{2} \theta}{b^{2}}}\left(e^{2} \cos ^{2} \theta-1\right)$
$\Rightarrow S M \cdot S' N=b^{2}=$ Constant
