By definition, a conic section is a curve obtained by intersecting a cone with a plane. In Algebra II, we work with four main types of conic sections: circles, parabolas, ellipses and hyperbolas. Each of these conic sections has different characteristics and formulas that help us solve various types of problems.
We're now going to talk about conic sections and conic sections are basically different shapes that are made when we take a plane through a cone okay? So basically what we have here are a number of different images to show you how these shapes are made.
The first one we've actually talked about and it's actually a parabola okay? So what happens if you have these two cones lying on top of each other you take a cone that is parallel to the edge of the cone you're actually going to end up just getting a cross section and that cross section is going to be a parabola okay?
If you take the plane parallel to the base of the cone, you end up with a perfect circle okay? If you end up taking this plane that is not parallel to the side or the bottom and it crosses through a cone what you end up with is an ellipse which is basically a fancy word for an oval.
And the last one is if we take this plane and we cross our two cones perpendicularly to the base, what we end up with is basically something that looks like two parabolas and that's kind of called a hyperbola okay? So basically we have these two cones and a plane crossing through them and we basically have 4 possible results; a parabola which you already know, a circle, ellipse and a hyperbola and together all those curves are called conic sections.