The equation of the circle concentric with the circle $x^{2} + y^{2} + 8 x + 10 y - 7 = 0$ and passing through the centre of the circle $x^{2} + y^{2} - 4 x - 6 y = 0$ is-

x^{2} + y^{2} + 8 x + 10 y + 59 = 0

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x^{2} + y^{2} + 8 x + 10 y - 59 = 0

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x^{2} + y^{2} - 4 x - 6 y + 87 = 0

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x^{2} + y^{2} - 4 x - 6 y - 87 = 0

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Solution

The correct option is D $x^{2} + y^{2} + 8 x + 10 y - 59 = 0$
Center of circle $x^{2} + y^{2} - 4 x - 6 y = 0$ is $(2, 3)$
Now equation of circle concentric with $x^{2} + y^{2} + 8 x + 10 y - 7 = 0$ is
$x^{2} + y^{2} + 8 x + 10 y + c = 0$
And as it passes through $(2, 3)$
Then $c = - 59$
$∴$ equation of circle would be $x^{2} + y^{2} + 8 x + 10 y - 59 = 0$

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