Explanation

(a)
Let general equation of a circle is
$x^{2} + y^{2} + 2gx + 2fy + c = 0$ …(i)
If the circle (i) cuts orthogonally each of the given three circles
Then, condition is
$2g_{1}g_{2} = 2f_{1}f_{2} = c_{1} + c_{2}$
Applying the condition one by one, we get
$2g + 17f = c + 4$ …(ii)
$7g + 6f = c + 11$ …(iii)
And $- g + 22f = c + 3$ …(iv)
On solving Eqs. (ii), (iii) and (iv), we get
$g = - 3,\ f = - 2$
Therefore, the centre of the circle is (3, 2)