- (a) Find the binomial expansion of \(( 2 - 3 x ) ^ { - 3 }\) in ascending powers of \(x\) up to and including the term in \(x ^ { 3 }\), simplifying each coefficient.
(b) State the set of values of \(x\) for which your expansion is valid.
- A curve has the equation
$$x ^ { 2 } + 3 x y - 2 y ^ { 2 } + 17 = 0$$
(a) Find an expression for \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) in terms of \(x\) and \(y\).
(b) Find an equation for the normal to the curve at the point \(( 3 , - 2 )\).