11 The point A has \(x\)-coordinate 5 and lies on the curve \(y = x ^ { 2 } - 4 x + 3\).
- Sketch the curve.
- Use calculus to find the equation of the tangent to the curve at A .
- Show that the equation of the normal to the curve at A is \(x + 6 y = 53\). Find also, using an algebraic method, the \(x\)-coordinate of the point at which this normal crosses the curve again.