13. The curve \(C\) has equation
$$y = \frac { ( x - 3 ) ( 3 x - 25 ) } { x } , \quad x > 0$$
- Find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) in a fully simplified form.
- Hence find the coordinates of the turning point on the curve \(C\).
- Determine whether this turning point is a minimum or maximum, justifying your answer.
The point \(P\), with \(x\) coordinate \(2 \frac { 1 } { 2 }\), lies on the curve \(C\).
- Find the equation of the normal at \(P\), in the form \(a x + b y + c = 0\), where \(a\), b and \(c\) are integers.
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