15. Tangents drawn from \( P(1,8) \) to the circle \( x^{2}+y^{2}-6 x-4 y-11=0 \) touches the circle at the points \( A \) and \( B \) respectively. If the radius of the circle which passes through the points of intersection of circles \( x^{2}+y^{2}-2 x-6 y+6=0 \) and \( x^{2}+y^{2}+2 x-6 y+6=0 \) and intersects the circumcircle of the \( \triangle PAB \) orthogonally is equal to \( \frac{\sqrt{ p }}{ q } \) where \( p , q \in N \), then find the minimum value of \( ( p + q ) \)
