Find the relation between the given quadric surfaces and conic sections.

Question

jlo2niT · Accepted Answer

Step 1
Quadric surfaces and conic sections.
As we know each conic section has two axes.

a x_{1}^{2} + 2 b x_{1} x_{2} + c x_{2}^{2} + {d x}_{1} + e x_{2} + f = 0

This is the quadratic equation in two variables of conic section,
Let us now consider

x_{1}

and

x_{2}

as two coordinate axes.

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

This is the same quadratic equation written in three variables,
Hence further the graph of this equation will be a quadric surface,
Where

x_{1}, x_{2}

and

x_{3}

are three coordinate axes.
Hence, quadric surfacess are the three-dimensional analogs of conic sections.

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