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When I was first introduced parabolas/hyperbolas, circles, and ellipses, I was shown how each and every one of them could be represented as conic sections - an intersection of a plane and a conic surface.

It made me wonder, whether the quadratic equations of parabolas, etc. themselves were actual equations of the intersection of said surfaces, or simply called conic sections because they looked the part.

In the case of the former, would someone please be kind enough to explain how it is so in simple enough terms so a person not so versed in the discipline could grasp the basics?

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  • $\begingroup$ Conic sections were probably originally defined as literally sections of a conic. It happens that they can indeed be expressed as quadratic curves, so they are exactly the same. $\endgroup$ – user21820 Jun 3 '15 at 7:27
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This question is answered in James Tanton's companion guide to quadratics. Although it is tempting to simply copy and paste his explanation here, that would be stealing! He clearly put a lot effort into making the explanation as accessible as possible and so I think he deserves the small compensation of not having his material stolen!

If you are quite new to this as you say you are, here is his open course on quadratics: http://gdaymath.com/courses/quadratics/

And the explanation you are looking for is in this book here: http://www.lulu.com/shop/james-tanton/companion-guide-to-quadratics/ebook/product-20965967.html

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