I want to plot a cone in 3-d for any given axis vecttor, center and eccentricity.

Given a  vector v (parallel to the principle axis) and a center point c,

and generating vectors u(beta) orthogonal to v for 0 < beta < 2pi,

and real positive parameters a and b 

I want to plot the hyperboloid  c + a*v*sec(alpha) + b*u(beta)*tan(alpha)

for -pi/2 < alpha < pi/2.

I am able to generate something of a plot, but can't control the size and appearance.