13. The circle \(C\) has centre \(A ( 1 , - 3 )\) and passes through the point \(P ( 8 , - 2 )\).
- Find an equation for the circle \(C\).
The line \(l _ { 1 }\) is the tangent to \(C\) at the point \(P\).
- Find an equation for \(l _ { 1 }\), giving your answer in the form \(y = m x + c\)
The line \(l _ { 2 }\), with equation \(y = x + 6\), is the tangent to \(C\) at the point \(Q\).
- Find the coordinates of the point \(Q\).