If (−3, 2) lies on the circle x² + y² + 2gx + 2fy + c = 0 which is concentric with the circle x² + y² + 6x + 8y − 5 = 0, then c =
(a) 11
(b) −11
(c) 24
(d) none of these

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Solution

(b) −11

The centre of the circle x² + y² + 6x + 8y − 5 = 0 is (−3, −4).

The circle x² + y² + 2gx + 2fy + c = 0 is concentric with the circle x² + y² + 6x + 8y − 5 = 0.
Thus, the centre of x² + y² + 2gx + 2fy + c = 0 is (−3, −4).
$∴ g = 3, f = 4$

Also, it is given that (−3, 2) lies on the circle x² + y² + 2gx + 2fy + 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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If (−3, 2) lies on the circle x2 + y2 + 2gx + 2fy + c = 0 which is concentric with the circle x2 + y2 + 6x + 8y − 5 = 0, then c = (a) 11 (b) −11 (c) 24 (d) none of these

If (−3, 2) lies on the circle x² + y² + 2gx + 2fy + c = 0 which is concentric with the circle x² + y² + 6x + 8y − 5 = 0, then c =
(a) 11
(b) −11
(c) 24
(d) none of these