Coordinate Geometry - Length of a Line Segment

A circle \(C\) passes through the point \(P \ (-6, 6)\) and has the same centre as the circle \(x^{2} + y^{2} + 6x - 4y + 2 = 0\).

1. Find the equation of the circle \(C\).
2. Find the equation of the tangent to the circle \(C\), at the point \( (-6,6) \).

Another point \(Q \ (-6, q)\) which lies on circle \(C\), is the same distance from the \(y\)-axis as the point \(P\).

4. Find the coordinates of the point \(Q\).
5. Find the perimeter of the triangle \(POQ\), where \(O\) is the centre of the circle \(C\).