Question

Graph the quadric surfaces given by the equations

$z=x^2-y^2$

Short answer

Draw the hyperbolic parabolic graph $z=x^2-y^2$as shown below.

Step-by-step solution

Introduction.

Quadric surfaces are described in two dimensions by quadratic equations. Quadrics include spheres, ellipsoids and cones.

Given Information.

Consider the following formula:

$z=x^2-y^2$

The goal is to create a graph of the quadric surface.

If $y=0,$then $z=x^2,$and the $xz-$plane intersects the surface in the form of a parabola.

Put $y=k,$then $z=x^2-k^2,$which represents the parabola that opens upward.

Likewise, if $x=k,$the trace is $z=k^2-y^2.$

This denotes a parabola that opens downward.

Explanation.

Draw the hyperbolic parabolic graph $z=x^2-y^2$as shown below.