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Question Number 38936 by ajfour last updated on 01/Jul/18

Commented by ajfour last updated on 01/Jul/18

$F i n d t h e l o c u s o f p o i n t P (t h e$ $p o i n t o f i n t e r s e c t i o n o f t a n g e n t s$ $t o e l l i p s e \frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1 . T h e t a n g e n t s$ $b e i n g d r a w n a t p o i n t s w h e r e a$ $c h o r d (d i s t a n c e d f r o m c e n t e r)$ $c u t s t h e e l l i p s e .$
	Answered by ajfour last updated on 01/Jul/18

	$l e t P \equiv (h, k)$ $E q . o f c h o r d i f c o n t a c t i s$ $\frac{h x}{a^{2}} + \frac{k y}{b^{2}} = 1$ $i t s d i s t a n c e f r o m o r i g i n i s d$ $\Rightarrow d = \frac{1}{\sqrt{\frac{h^{2}}{a^{4}} + \frac{k^{2}}{b^{4}}}}$ $H e n c e l o c u s i s$ $\frac{x^{2}}{a^{4}} + \frac{y^{2}}{b^{4}} = \frac{1}{d^{2}} .$
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