The parametric equations for a parabola with focus at (Fx, Fy)
and focal parameter 2a
, in terms of angle, would be:
x = Fx + (2*a*cos(ang))/(1 + cos(ang))
y = Fy + (2*a*sin(ang))/(1 + cos(ang))
Not too bad. :) You can adjust a
as needed. You can actually modify it a bit by adjusting the ratio of the distances from the focus to the plot, versus the plot to the directrix:
x = Fx + (2*a*cos(ang))/(1 + cos(ang))
y = Fy + (2*b*sin(ang))/(1 + cos(ang))
Here the ratio will be b/a
. So you can have the same distance from the origin to the vertex (2a) and make b
larger to "flatten" the parabola.