7 A line has equation \(y = 2 x\) and a circle has equation \(x ^ { 2 } + y ^ { 2 } + 2 x - 16 y + 56 = 0\).
- Show that the line does not meet the circle.
- (a) Find the equation of the line through the centre of the circle that is perpendicular to the line \(y = 2 x\).
(b) Hence find the shortest distance between the line \(y = 2 x\) and the circle, giving your answer in an exact form.