Equation of a closure of a cone

Jan 2020
San Antonio
let f(x,y) = 0 be the equation of a curve X in R^2, and suppose that Df(x,y) =/= 0 for all (x,y) in X.

a) find an equation for the closure of the cone CX in R^3 over X, when CX is the union of all the lines through the origin and points (x,y,1) with (x,y) in X.
b) if X has equation y = x^3 what is the equation of the closure of CX?