Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2016 / Paper 2 / 12 / a / Solution

Put $R=|b|$ so that the radial range respects the stated allowance $b\ne 0$. With the azimuth measured from the starting meridian, the cylindrical coordinates of the curved surface satisfyAt $r=0$ all azimuths describe the same apex. The surface is a sector of an elliptic paraboloid.