While I was reading about conic sections, I came across the following statement:
A parabola is an ellipse, but with one focal point at infinity.
But it is not clear to me. Can someone explain it clearly?
The equation for an ellipse with a focus at (0,0) and the other at (0,2ae) keeping a(1−e)=f (where f is distance from the vertex to the focus of the ellipse, which ends up being the focal length of the parabola) is
which is equivalent to
If we let a→∞ (and therefore e=1−fa→1), we get
which is a parabola.