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(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

x2a2(1−e2)+(y−ae)2a2=1

which is equivalent to

x2f(1+e)+y2−2aeya=f(1+e)

If we let a→∞ (and therefore e=1−fa→1), we get

y=x24f−f

which is a parabola.

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