N1995 P2 Q12 [Modified]

A curve is defined parametrically by \(x=\frac{5}{2}\cos \theta ,\,\,y=\frac{3}{2}\sin \theta \,\,,\)for \(0\le \theta \le 2\pi \).

1. Find the coordinates of the axial intercepts algebraically.[2]
2. Show that the Cartesian equation of the curve is \(\frac{{{x}^{2}}}{25}+\frac{{{y}^{2}}}{9}=\frac{1}{4}\).[2]
3. Show that the distance of the point \(P\) on the curve with parameter \(p\) to the point \((2,0)\) is \(\frac{5}{2}-2\cos \,p\). Find a similar expression for the distance between \(P\) and \((-2,0)\).[3]