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Question Number 29332 by Tinkutara last updated on 07/Feb/18

	Answered by ajfour last updated on 07/Feb/18

	$l e t e q . o f c i r c l e b e$ $x^{2} + y^{2} + 2 g x + 2 f y = 0 (c = 0)$ $f o r t w o c i r c l e s t o c u t o r t h o g o n a l l y$ $2 g_{1} g_{2} + 2 f_{1} f_{2} = c_{1} + c_{2}, s o$ $- 4 g + 6 f = 10, a n d$ $12 f = 6 \Rightarrow 2 f = 1$ $a n d 2 g = - \frac{7}{2}$ $e q . o f c i r c l e i s t h e r e f o r e$ $x^{2} + y^{2} - \frac{7 x}{2} + y = 0$ $o r 2 x^{2} + 2 y^{2} - 7 x + 2 y = 0 .$
	Commented by ajfour last updated on 08/Feb/18

	$i s i t c o r r e c t, i f s o d i d y o u f o l l o w ?$
	Commented by Tinkutara last updated on 08/Feb/18
	Yes correct surely Thanks! But if we don't remember this condition we can't do this? Are we to learn all these conditions in Conic Sections?
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