8 The equation of a circle is \(x ^ { 2 } + y ^ { 2 } + p x + 2 y + q = 0\), where \(p\) and \(q\) are constants.
- Express the equation in the form \(( x - a ) ^ { 2 } + ( y - b ) ^ { 2 } = r ^ { 2 }\), where \(a\) is to be given in terms of \(p\) and \(r ^ { 2 }\) is to be given in terms of \(p\) and \(q\).
The line with equation \(x + 2 y = 10\) is the tangent to the circle at the point \(A ( 4,3 )\). - Find the equation of the normal to the circle at the point \(A\).
- Find the values of \(p\) and \(q\).