10. The curve \(C\) has equation
$$x = 3 \sec ^ { 2 } 2 y \quad x > 3 \quad 0 < y < \frac { \pi } { 4 }$$
- Find \(\frac { \mathrm { d } x } { \mathrm {~d} y }\) in terms of \(y\).
- Hence show that
$$\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { p } { q x \sqrt { x - 3 } }$$
where \(p\) is irrational and \(q\) is an integer, stating the values of \(p\) and \(q\).
- Find the equation of the normal to \(C\) at the point where \(y = \frac { \pi } { 12 }\), giving your answer in the form \(y = m x + c\), giving \(m\) and \(c\) as exact irrational numbers.
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