Let S be the cone z = myc- ty-, m >0. (a) Write a parametric equation of S using the polar coordinates (r, #) as the parameters. (b) A curve C on S can be described as r = f(0). Write down the arclength integral for C. (c) Show that if C is a geodesic then f(0) must satisfy the differential equation (1 + m] ja fo = $2(f2 -a?) for some suitable constant a