The circles x^2 +y^2 −2ax+8y+13=0 and x^2 +y^2 +2x+2by+1=0 are congruent. If they are 2(√(10)) units apart, find the possible values of a and b.


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Question Number 174094 by nadovic last updated on 24/Jul/22

$The circles x^{2} + y^{2} - 2 a x + 8 y + 13 = 0$ $and x^{2} + y^{2} + 2 x + 2 b y + 1 = 0 are$ $congruent . If they are 2 \sqrt{10} units$ $apart, find the possible values of$ $a and b .$
	Answered by a.lgnaoui last updated on 25/Jul/22

	${(x - a)}^{2} + {(y + 4)}^{2} = a^{2} + 3 (C 1)$ ${(x + 1)}^{2} + {(y + b)}^{2} = b^{2} (C 2)$ $C 1 a n d C 2 a r e c o n g r u a n t s t h e n$ $a^{2} + 3 = b^{2} \Rightarrow b = \sqrt{a^{2} + 3} (a, b) ϵ R^{2}$ $e x e m p l e a = 1 b = 2$ $a = 0 b = \sqrt{3}$ $. . . . . . . . . . .$
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