1. ## level curves

Sketch the level curves z = c for z = x^2/y , c=-4,-1,0,1,4

Sketch the level curves z = c for z = x^2/y , c=-4,-1,0,1,4
The level curves are obtained by setting z =-4, -1 0 1 and 4 so we simply draw the functions

$
y = - \frac{x^2}{4},\;\;
y = - x^2
\;\;
y = x^2
\;\;
y = \frac{x^2}{4}
$

3. Setting c equal to -4,-1,1,4 we obtain...

$y= - \frac{x^{2}}{4}, y= - x^{2}, y= x^{2}, y= \frac{x^{2}}{4}$

... good!... and setting, as also requested, c=0? ...

Kind regards

$\chi$ $\sigma$

4. Thanks are undeserved since my observations were quite obvious... also quite obvious is that the level curve for $c=0$ is $x=0$, i.e. the level curve is the y-axis...

Kind regards

$\chi$ $\sigma$