If you slice a cone at a diagonal, you get an ellipse:
 

Here's what geometrically makes an ellipse an ellipse:

You start with the two green dots...

So, if you put two nails on a board and put a loop of string around them...

You can draw a perfect ellipse! Just keep the string pulled tightly.

Think about it... That loop of string will always be the same length -- won't it?

That's what makes an ellipse!