Answer
The level curves are hyperbolas of the form $xy=c$
Work Step by Step
We have $f(x,y)=xy$
Then, we equalize the equation $f(x,y)=c$
So,
For $c=1$, $y=\frac{1}{x}$
For $c=2$, $y=\frac{2}{x}$
For $c=3$, $y=\frac{3}{x}$
For $c=4$, $y=\frac{4}{x}$
For $c=5$, $y=\frac{5}{x}$
For $c=6$, $y=\frac{6}{x}$
For $c=-1$, $y=-\frac{1}{x}$
For $c=-2$, $y=-\frac{2}{x}$
For $c=-3$, $y=-\frac{3}{x}$
For $c=-4$, $y=-\frac{4}{x}$
For $c=-5$, $y=-\frac{5}{x}$
For $c=-6$, $y=-\frac{6}{x}$
