10 A circle has centre \(C ( - 2,4 )\) and radius 5 .
- Find the equation of the circle, giving your answer in the form \(x ^ { 2 } + y ^ { 2 } + a x + b y + c = 0\).
- Show that the tangent to the circle at the point \(P ( - 5,8 )\) has equation \(3 x - 4 y + 47 = 0\).
- Verify that the point \(T ( 3,14 )\) lies on this tangent.
- Find the area of the triangle \(C P T\).
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