The equation of circle passing through $(3, 6)$ touching both the axes is
$x^{2} + y^{2} + 6 x + 12 y + 16 = 0$
$x^{2} + y^{2} - 6 x - 6 y + 9 = 0$
$x^{2} + y^{2} + 30 x + 30 y + 225 = 0$
$x^{2} + y^{2} + 45 x - 16 y + 225 = 0$

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Solution

The correct option is B $x^{2} + y^{2} - 6 x - 6 y + 9 = 0$
The equation of circle touching both axes is
$x^{2} + y^{2} - 2 p x - 2 p y + p^{2} = 0$ ________ (1)
since, the circle passes through point (3+6)
Therefore , $(3)^{2} + (- 6)^{2} - 2 p \times 3 - 2 p \times 6 + p^{2} = 0$
$9 + 36 - 6 p - 12 p + p^{2} = 0$
$45 - 8 p + p^{2} = 0$
p=15,3
Hence, equation of the circle will be
$x^{2} + y^{2} - 6 x - 6 y + 9 = 0$ or $x^{2} + y^{2} - 30 x - 30 y + 225 = 0$

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