= Solution
For a nonzero level $h$, completing the square gives
$$
\boxed{\left(x-\frac1{2h}\right)^2+\left(y-\frac1{2h}\right)^2=\frac1{2h^2}-1.}
$$
Thus the <level sets of a linear numerator over a radial quadratic> are circles centred on $y=x$, real only for $0<|h|\leq1/\sqrt2$. The extreme levels shrink to points. The zero contour is the straight line $x+y=0$, separating positive and negative heights; near it, small nonzero levels are large circles. Heights tend to zero at infinity.
\Image[/past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2006/paper-2-rational-height-contours.png]
{title=Circular nonzero contours around the two extrema of a rational height function}
{description=Original contour plot. Blue positive and orange negative circles surround the marked maximum and minimum; the black line is the zero contour. Circle centres lie on $y=x$.}
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