Parametric equation of a cone. 
I have a cone with vertex (a, b, c) and base circumference with center $(x_0,y_0)$ and radius R. I can't understand what is the parametric representation of three dimensional space inside the cone. Any suggestions please?

Begin with a parametric representation of the base, using polar coordinates (with the center shifted to $(x_0,y_0)$. For any given point inside the cone, draw a straight line from the vertex through the point to the base of the cone. Let two parameters specify the latter point. Use $z$ as the third parameter, or perhaps a variable $t$ that varies linearly with $z$ so that $t=0$ at the vertex and $t=1$ at the base of the cone. Many minor variations over this theme are possible.
