If (-3, 2) lies on the circle $x^{2} + y^{2} + 2 g x + 2 f y + c = 0$ which is concentric with the circle $x^{2} + y^{2} + 6 x + 8 y - 5 = 0$ , then c=

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-11

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None of these

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Solution

The centre of the circle $x^{2} + y^{2} + 6 x + 8 y - 5 = 0$ is (-3, -4)

The circle $x^{2} + y^{2} + 2 g x + 2 f y, + c = 0$ is concentric with the circle $x^{2} + y^{2} + 6 x + 8 y - 5 = 0$

$∴ g = 3, f = 4$

Also, it is given that (-3, 2) lies on the circle
$x^{2} + y^{2} + 2 g x + 2 f y + c = 0$

$∴ (- 3)^{2} + 2^{2} + 2 (3) (- 3) + 2 (4) (2) + c = 0$

$\Rightarrow 9 + 4 - 18 + 16 + c = 0$

$\Rightarrow c = - 11$

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