9 The curve \(y = ( x - 1 ) ^ { 2 }\) maps onto the curve \(\mathrm { C } _ { 1 }\) following a stretch scale factor \(\frac { 1 } { 2 }\) in the \(x\)-direction.
- Show that the equation of \(\mathrm { C } _ { 1 }\) can be written as \(y = 4 x ^ { 2 } - 4 x + 1\).
The curve \(\mathrm { C } _ { 2 }\) is a translation of \(y = 4.25 x - x ^ { 2 }\) by \(\binom { 0 } { - 3 }\).
- Show that the normal to the curve \(\mathrm { C } _ { 1 }\) at the point \(( 0,1 )\) is a tangent to the curve \(\mathrm { C } _ { 2 }\).