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

Carol Gates

Carol Gates

Answered question

2021-08-15

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

Answer & Explanation

jlo2niT

jlo2niT

Skilled2021-08-16Added 96 answers

Step 1
Quadric surfaces and conic sections.
As we know each conic section has two axes.
ax12+2bx1x2+cx22+dx1+ex2+f=0
This is the quadratic equation in two variables of conic section,
Let us now consider x1 and x2 as two coordinate axes.
ax12+bx22+cx32+2dx1x2+2ex1x3+2fx2x3+gx1+hx2+ix3+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 x1, x2 and x3 are three coordinate axes.
Hence, quadric surfacess are the three-dimensional analogs of conic sections.

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