5 A circle has equation \(( x - 2 ) ^ { 2 } + y ^ { 2 } = 20\).
- Write down the radius of the circle and the coordinates of its centre.
- Find the points of intersection of the circle with the \(y\)-axis and sketch the circle.
- Show that, where the line \(y = 2 x + k\) intersects the circle,
$$5 x ^ { 2 } + ( 4 k - 4 ) x + k ^ { 2 } - 16 = 0$$
- Hence find the values of \(k\) for which the line \(y = 2 x + k\) is a tangent to the circle.