A circle $x^{2} + y^{2} + 2 g x + 2 f y + c = 0$ passing through (4, 2) is concentric to the circle $x^{2} + y^{2} - 2 x + 4 y + 20 = 0,$ then the value of c will be

-4

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Solution

The correct option is A -4
Circle $x^{2} + y^{2} + 2 g x + 2 f y + c = 0$ is concentric with $x^{2} + y^{2} - 2 x + 4 y + 20 = 0.$ Therefore centre is (1, -2) and radius
$= \sqrt{g^{2} + f^{2} - c} = \sqrt{(1 - 4)^{2} + (- 2 + 2)^{2}} \Rightarrow c = - 4.$

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