- The curve \(C\) has equation
$$p x ^ { 3 } + q x y + 3 y ^ { 2 } = 26$$
where \(p\) and \(q\) are constants.
- Show that
$$\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { a p x ^ { 2 } + b q y } { q x + c y }$$
where \(a\), \(b\) and \(c\) are integers to be found.
Given that
- the point \(P ( - 1 , - 4 )\) lies on \(C\)
- the normal to \(C\) at \(P\) has equation \(19 x + 26 y + 123 = 0\)
- find the value of \(p\) and the value of \(q\).