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!)