How to find the Projection of a parabola on a plane with the intersection of a conic

Question

I'm trying to plot the conic intersection of a plane and a cone in python. I have a plane that is defined as x, y, z=0 and I have a unit vector and an angle at some height which I want to generate a cone from that angle extending out of the unit vector. Then where the extended cone and plane intersect I am interested in the projection of the intersection between the cone and plane. I would expect with angles at around 45 degrees that the projection would be a parabola. I'm trying to plot this in python. I think for the plane I would create a meshgrid for x,y within some bounds, and leave z=0. But I'm not sure how to create an array of points for the cone. If I had that my goal would then to look at the points of intersection between the x_plane, y_plane, and x_cone,y_cone to extract a 2D array of x's and y's that are the data points of the conic intersection, which should be able to be plotted with plt.plot() to get a parabola?