Quadric Surfaces How are quadric surfaces and conic sections related?

Conic sections
asked 2021-02-08
Quadric Surfaces How are quadric surfaces and conic sections related?

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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, \(ax_1^2 + 2bx_1x_2 + cx_2^2 + dx^1 ex_2 + f = 0\) 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: \(ax_1^2 + bx_2^2 + cx_3^2 + 2dx_1 x^2 + 2ex_1 x_3 + 2f_{x2x3} + gx_1 hx_2 ix_3 + j =0\) 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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