The equation of a circle is \(x^2+y^2+ax+by-12=0\). The points \(A(1,1)\) and \(B(2,-6)\) lie on the circle.

(a) Find the values of a and b and hence find the coordinates of the centre of the circle. [4]

(b) Find the equation of the tangent to the circle at the point A, giving your answer in the form \(px+qy=k\), where \(p,q,k\) are integers. [4]