Explanation

(c)
Let the equation of circle be
$x^{2} + y^{2} + 2gx + 2fy + c = 0$ …(i)
Since, circle (i) cuts the given circle orthogonally
$\therefore\ \ \ 2( - g)(3) + 2( - f)( - 2) = c - 3$
$\Rightarrow \ \ - 6g + 4f = c - 3$ …(ii)
Also, Eq. (i) passes through (3, 0)
$\therefore\ \ 3^{2} + 0^{2} + 2g(3) + 2f(0) + c = 0$
$\Rightarrow \ \ \ 6g + c + 9 = 0$ …(iii)
As Eq. (i) touches $y$-axis
$\therefore\ \ \ | - f| = \sqrt{g^{2} + f^{2} - c}$
$\Rightarrow \ \ \ g^{2} = c$ …(iv)
From Eqs. (iii) and (iv), we get
$g = - 3$ and $c = 9$
$\therefore$ From Eq. (ii),
$- 6( - 3) + 4f = 9 - 3\ \ \Rightarrow \ \ \ f = - 3$
$\therefore$ Required equation of circle is
$x^{2} + y^{2} - 6x - 6y + 9 = 0$