There is a conic-section with this implicit form:
$$ f(x,y) = ax^2 + 2bxy + cy^2 + 2dx + 2ey + f = 0 $$
I would like to write a program, which draws it, but I have no idea where to start. I could use a brute-force method, calculate it for each pixel, and the point is on the curve, if the value is around zero. But I am looking for a better solution.