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EunoR

Answered question

2021-02-08

Quadric Surfaces How are quadric surfaces and conic sections related?

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StrycharzT

Skilled2021-02-09Added 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, $a x_{1}^{2} + 2 b x_{1} x_{2} + c x_{2}^{2} + d x^{1} e x_{2} + f = 0$ 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: $a x_{1}^{2} + b x_{2}^{2} + c x_{3}^{2} + 2 d x_{1} x^{2} + 2 e x_{1} x_{3} + 2 f_{x 2 x 3} + g x_{1} h x_{2} i x_{3} + j = 0$ 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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