Ya know what you get if you slice a cone parallel to the edge?

Our old friend the parabola!

Here's what makes the parabola special -- geometry-wise:

 The green dot is a focus.

Just like with ellipses, the focus is a special place...

Some comets shoot through our solar system along parabolic paths with the Sun at the focus.

Notice how the comet speeds up as it gets closer to the Sun... It's a gravity thing!

(And, no, I didn't screw up on the comet's tail. The solar wind always blows the tail away from the Sun. By the way, I highly recommend that you take an astronomy class in college. You'll love it!)