Obtain an expression for the area of a closed oval curve of polar equation \(r=r(\theta)\) in the two cases when the pole (\(r=0\)) is inside the curve and when it is outside the curve. A circle of radius \(a\) has centre \(C\), and a point \(O\) is taken at distance \(c (< a)\) from its centre. The foot of the perpendicular from \(O\) to a tangent to the circle is \(P\). Show that the locus of \(P\) is a closed curve of area \(\pi(a^2+\frac{1}{2}c^2)\).