Find the equation of the circle concentric with the circle $x^{2} + y^{2} - 4 x - 6 y - 3 = 0$ and which touches the y-axis.

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Solution

Centre of the given circle is (2, 3).

Centre of the required circle is (2, 3).

The required circle touches the y-axis, so its radius = 2.

$∴$ the required equation is $(x - 2)^{2} + (y - 3)^{2} = 2^{2} .$

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x^{2} + y^{2} - 4 x - 6 y - 3 = 0

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Find the equation of the circle concentric with
$x^{2} + y^{2} - 4 x - 6 y - 3 = 0$
and which touches the y-axis.

x^{2} + y^{2} + 8 x + 10 y - 7 = 0

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