Answer
See image:
Work Step by Step
Level curves have the form:
$k=\displaystyle \frac{y}{x^{2}+y^{2}}$
$x^{2}+y^{2}=\displaystyle \frac{y}{k}$
$x^{2}+(y^{2}-\displaystyle \frac{1}{k}y)=0$
$x^{2}+(y^{2}-\displaystyle \frac{1}{k}y+(\frac{1}{2k})^{2})-(\frac{1}{2k})^{2}=0$
$x^{2}+(y-\displaystyle \frac{1}{2k})^{2}=\frac{1}{4k^{2}}$
(circles around ($0, \displaystyle \frac{1}{2k}) $with radius $\displaystyle \frac{1}{2k}$
For graphing,
$y=\displaystyle \pm\sqrt{\frac{1}{4k^{2}}-x^{2}}+\frac{1}{2k}$
