# Quadric Surfaces How are quadric surfaces and conic sections related?

EunoR 2021-02-08 Answered
Quadric Surfaces How are quadric surfaces and conic sections related?
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## Expert Answer

StrycharzT
Answered 2021-02-09 Author has 102 answers

Given: Quadric surfaces and conic sections. Each conic section has two axes and the quadratic equation in two variables of conic section is generally represented as, $a{x}_{1}^{2}+2b{x}_{1}{x}_{2}+c{x}_{2}^{2}+d{x}^{1}e{x}_{2}+f=0$ Here, ${x}_{1}$ and ${x}_{2}$ can be considered as two coordinate axes. Now, if the same quadratic equation is written in three variables, it will be as follows: $a{x}_{1}^{2}+b{x}_{2}^{2}+c{x}_{3}^{2}+2d{x}_{1}{x}^{2}+2e{x}_{1}{x}_{3}+2{f}_{x2x3}+g{x}_{1}h{x}_{2}i{x}_{3}+j=0$ The graph of this equation will be a quadric surface where x1, x and xy are three coordinate axes. Hence, quadric surfacesare the three-dimensional analogs of conic sections.

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