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-

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}

\dots \dots \dots . .