If $(- 3, 2)$ lies co 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 is equal to

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-11

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100

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Solution

The correct option is B -11
Equation of family of concentric circles to the circle $x^{2} + y^{2} + 6 x + 8 y - 5 = 0$ is $x^{2} + y^{2} + 6 x + 8 y + X = 0$
which is similar to $x^{2} + y^{2} + 2 g x + 2 f y + c = 0$
Thus, the point (-3, 2) lies on the circle
$x^{2} + y^{2} + 6 x + 8 y + c = 0$
$∴ (- 3)^{2} + (2)^{2} + 6 (- 3) + 8 (2) + c = 0$
$\Rightarrow 9 + 4 - 18 + 16 + c = 0 \Rightarrow c = - 11$
Hence, option B is correct.

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If (−3,2) lies co the circle x2+y2+2gx+2fy+c=0, which is concentric with the circle x2+y2+6x+8y−5=0, then c is equal to

If $(- 3, 2)$ lies co 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 is equal to