Coordinate Geometry - Tangents and Normals to Circles

The equation of the circle \({{C}_{1}}\) is given by \({{x}^{2}}+{{y}^{2}}-10x+6y+30=0\).

1. Find the coordinates of its center and the length of its radius.
2. Show that the circle \({{C}_{1}}\) touches the line \(x=3\).
3. The circle, \({{C}_{1}}\) is reflected about the line\(x=1\). Find the equation of the reflected circle, \({{C}_{2}}\).
4. Find the equation of another circle \({{C}_{3}}\) which has an area that is \(4\) times larger than \({{C}_{1}}\) and its center at the origin.