Hey highlat.

Recall that a cone in its cross section is just a circle and a circle has a standard parametrization involving an angle (call it t) and a radius r.

If the radius is proportional to the height of the cone and the the height and angle are independent parameters (you will have since the cone is two-dimensional like taking a piece of paper and folding it), then can you find the parametrization?

(Hint: If you don't know the parametrization of a circle, think about how a circle is defined with trig functions).