# 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?

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
If we let $a\to\infty$ (and therefore $e=1-\frac fa\to1$), we get
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