If p, p¹ denote the lengths of the perpendiculars from the focus and the centre of an ellipse with semi major axis of length 'a ' respectively on a tangent to the ellipse and r denote the focal distance of the point, then

Equation of the ellipse is $\frac{{\mathrm{x}}^2}{{\mathrm{a}}^2}+\frac{{\mathrm{y}}^2}{{\mathrm{b}}^2}=1$    …..(1)
Equation of tangent at P($\mathrm{\theta }$) is $\frac{\mathrm{x}}{\mathrm{a}}\cos \mathrm{\theta }+\frac{\mathrm{y}}{\mathrm{b}}\sin \mathrm{\theta }-1=0\to \left(2\right)$
$p=perpendicular$ distance from $\mathrm{S}(\mathrm{ae},0)\text{ to }\left(2\right)$

$p=\frac{1-e\cos \theta }{\sqrt{{\displaystyle \frac{{\cos }^2\theta }{a^2}}+{\displaystyle \frac{{\sin }^2\theta }{b^2}}}}$

p'=perpendicular distance from (0, 0) to (2)

$p\text{'}=\frac{1}{\sqrt{{\displaystyle \frac{{\cos }^2\theta }{a^2}}+{\displaystyle \frac{{\sin }^2\theta }{b^2}}}}$

and $r=SP=a(1-e\cos \theta )$

Now  $p=\frac{\mathrm{r}}{\mathrm{a}}\cdot p^1\Rightarrow \mathrm{ap}={\mathrm{rp}}^1$