Conic Sections

Conic Section: a section (or slice) through a cone.

Did you know that by taking different slices through a cone you can create a circle, an ellipse, a parabola or a hyperbola?

Cones	Circle	Ellipse	Parabola	Hyperbola

	straight through	slight angle	parallel to edge of cone	steep angle

So all those curves are related!

General Equation

In fact, we can make an equation that covers all these curves.

Because they are plane curves (even though cut out of the solid) we only have to deal with Cartesian ("x" and "y") Coordinates.

But these are not just straight lines, so just "x" and "y" will not do ... we need to go to the next level, and have x² and y², and also x (without y), y (without x), x and y together (xy) and a constant term.

We also need factors (A,B,C etc) so the general equation that covers all conic sections is:

And from that equation we can create equations for the circle, ellipse, parabola and hyperbola ... but that is beyond the scope of this page.