A circle is defined by the parametric equations \(x = 3 + 2 \cos \theta , y = - 4 + 2 \sin \theta\).
Find a cartesian equation of the circle.
Write down the centre and radius of the circle.
In this question you must show detailed reasoning.
The curve \(S\) is defined by the parametric equations \(x = 4 \cos t , y = 2 \sin t\). The line \(L\) is a tangent to \(S\) at the point given by \(t = \frac { 1 } { 6 } \pi\).
Find where the line \(L\) cuts the \(x\)-axis.