Parabola is an ellipse, but with one focal point at infinity

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?

Answer

The equation for an ellipse with a focus at (0,0) and the other at (0,2ae) keeping a(1e)=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
x2a2(1e2)+(yae)2a2=1
which is equivalent to
x2f(1+e)+y22aeya=f(1+e)
If we let a (and therefore e=1fa1), we get
y=x24ff
which is a parabola.

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Attribution
Source : Link , Question Author : Kumar , Answer Author : robjohn

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