10.
a. The parametric equations of a curve are \(x = \theta \cos \theta\) and \(y = \sin \theta\) Find the gradient of the curve at the point for which \(\theta = \pi\)
b. A curve is defined parametrically by the equations; $$x = \cos \theta \quad y = \left( \frac { \sin \theta } { 2 } \right) \left( \sin \frac { \theta } { 2 } \right)$$ Show that the cartesian equation of the curve can be written as \(y ^ { 2 } = \frac { 1 } { 8 } ( 1 - x ) ^ { 2 } ( 1 + x )\)