Suppose we want to plot the level set curves of a multivariable function such as $z=f(x,y)=\frac{y}{x}$, if we decide to draw its contours then we should equate a constant value for the function with the function, i.e. to find the intersection of a horizontal plane like $z=c$ with the 3D plot. However, if we want to explicitly derive the equations for the 2D contour plots instead of geometrically intersecting the $z=c$ plane with the $f(x,y)$ plot, then I get into a perplexing situation where $c=\frac{y}{x}$ reduces to $y=cx$ and that does not correspond to the curvy contour plots of $z=f(x,y)=\frac{y}{x}$
