12 A circle has equation \(x ^ { 2 } + y ^ { 2 } - 8 x - 4 y = 9\).
- Show that the centre of this circle is \(\mathrm { C } ( 4,2 )\) and find the radius of the circle.
- Show that the origin lies inside the circle.
- Show that AB is a diameter of the circle, where A has coordinates (2, 7) and B has coordinates \(( 6 , - 3 )\).
- Find the equation of the tangent to the circle at A . Give your answer in the form \(y = m x + c\).