Carl Horowitz

University of Michigan
Runs his own tutoring company

Carl taught upper-level math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!

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Introduction to Conic Sections - Problem 1

Introduction to Conic Sections - Concept

Carl Horowitz
Carl Horowitz

University of Michigan
Runs his own tutoring company

Carl taught upper-level math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!

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In Algebra, we often use the rectangular coordinate system to graph lines, parabolas and other formulas. Important terms to be familiar with include the y-axis, the x-axis, y-coordinates, x-coordinates and points.The rectangular coordinate system can also be called the coordinate system or the x-y axis.

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.