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.