10 A circle has equation \(( x - 5 ) ^ { 2 } + ( y + 2 ) ^ { 2 } = 25\).
- Find the coordinates of the centre \(C\) and the length of the diameter.
- Find the equation of the line which passes through \(C\) and the point \(P ( 7,2 )\).
- Calculate the length of \(C P\) and hence determine whether \(P\) lies inside or outside the circle.
- Determine algebraically whether the line with equation \(y = 2 x\) meets the circle.
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