Q. 47 - Calculus

Question

Graph the quadric surfaces given by the equations 

$z=x^2-y^2$

Step-by-Step Solution

Answer

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

Step1: Introduction.

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

Step2: 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.

Step3: Explanation.

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