Draw the level curves

Question

Draw the level curves

Z=x^2-y^2

Answer 1

This is the hyperbolic paraboloid. See a picture in your Calculus book.

You are getting the level curves by setting z equal c a constant to any value in the range of the function , in our case all real numbers.

A. If c< 0

You are getting all the hyperbolas with the transverse axis, the line that connects the foci, on the y-axis.

For example if c = 4 you get the hyperbola y² / 4 - x² / 4 = 1

B. If c = 0 then x² = y² that is two lines y = ± x

C. If c> 0

You are getting all the hyperbolas with the transverse axis, the line that connects the foci, on the x-axis.

For example if c = 4 you get the hyperbola x² / 4 - y² / 4= 1