14 A curve has polar equation \(\mathrm { r } = \mathrm { a } ( \cos \theta + 2 \sin \theta )\), where \(a\) is a positive constant and \(0 \leqslant \theta \leqslant \pi\).
- Determine the polar coordinates of the point on the curve which is furthest from the pole.
- Show that the curve is a circle whose radius should be specified.
- Write down the polar coordinates of the centre of the circle.