- The curve \(C\) has equation
$$2 x ^ { 2 } y + 2 x + 4 y - \cos ( \pi y ) = 17$$
- Use implicit differentiation to find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) in terms of \(x\) and \(y\).
The point \(P\) with coordinates \(\left( 3 , \frac { 1 } { 2 } \right)\) lies on \(C\).
The normal to \(C\) at \(P\) meets the \(x\)-axis at the point \(A\). - Find the \(x\) coordinate of \(A\), giving your answer in the form \(\frac { a \pi + b } { c \pi + d }\), where \(a , b , c\) and \(d\) are integers to be determined.