Give a rough sketch of the curve whose coordinates are given by \[ \begin{cases} x = a\phi+b\sin\phi, \\ y = b(1-\cos\phi), \end{cases} \] where \(\phi\) is a parameter, and \(a>b>0\). Find the equation of the normal at any point and show that the coordinates of the centre of curvature are \begin{align*} x &= a\phi - b\sin\phi - (a^2-b^2)\frac{\sin\phi}{b+a\cos\phi}, \\ y &= 3a+b-\frac{b^2}{a}+b\cos\phi + \frac{(a^2-b^2)^2}{ab}\frac{1}{b+a\cos\phi}. \end{align*}