If you want to find a parametric equation to Ax+By+Cz+D=0 follow these steps:
1. find 3 points on the plane Ax+By+Cz+D=0 (you can take x=y=0, then find z\ Say that (A,B,C) is your normal then (A,B,C)(a,b,c)=0 )
2. Suppose that 3 points are A, B and C. Create two vectors AB and AC.
3. Construct your parametric equation: (point on a plane)+vec(AB)*t +vec(AC)*s