consider an ellipse with foci $(x_a,y_a)$ and $(x_b,y_b)$ such that $\sqrt{(x-x_a)^2+(y-y_a)^2}+\sqrt{(x-x_b)^2+(y-y_b)^2}=p$
consider a line parallel to the line through their foci, e.g. $y=\frac{y_b-y_a}{x_b-x_a}x+q$
find the points of intersection
is there a quick way to do this by converting the equation for the ellipse into a conic equation?
cheers, dave xx