4. A curve is given parametrically by the equations
$$x = 5 \cos t , \quad y = - 2 + 4 \sin t , \quad 0 \leq t < 2 \pi$$
- Find the coordinates of all the points at which \(C\) intersects the coordinate axes, giving your answers in surd form where appropriate.
- Sketch the graph at \(C\).
\(P\) is the point on \(C\) where \(t = \frac { 1 } { 6 } \pi\). - Show that the normal to \(C\) at \(P\) has equation
$$8 \sqrt { } 3 y = 10 x - 25 \sqrt { } 3$$