10 The equation of a circle is \(( x - a ) ^ { 2 } + ( y - 3 ) ^ { 2 } = 20\). The line \(y = \frac { 1 } { 2 } x + 6\) is a tangent to the circle at the point \(P\).
- Show that one possible value of \(a\) is 4 and find the other possible value.
- For \(a = 4\), find the equation of the normal to the circle at \(P\).
- For \(a = 4\), find the equations of the two tangents to the circle which are parallel to the normal found in (b).