(a) Let P be a point on a smooth curve r=f() in R2 which is not the origin, and let be the acute angle between the line OP and the tangent to the curve at P. Show thatcos=|f'()|f()2f'()22(b) Using (a), show that at every point P on the curve r=e, the angle between the line OP and the tangent line to the curve at P is always 4.(c) Let r=f() be a smooth curve such that at every point P on it, the angle between the line OP and the tangent line to the curve at P is always a fixed constant. Show that there exist constants C and k such that f()=Cek for all .