A general quadric has equation
Ax2 + By2 + Cz2 + Dxy + Eyz + Fxz + Gx + Hy +Iz + J =0
Intersections with general quadrics are computed in a way similar to cones and cylinders: for a ray p+ v t, take x = px + vx t, y = py + vy t, y = pz + vzt,
and solve the equation for t; if there are solutions,
take the smaller nonnegative one.
Infinite cones and cylinders are special cases of general quadrics.