= Solution
The zero <level set> consists of the lines $x=1$ and $y=0$. The height is positive where $(x-1)y>0$ and negative where that product is negative. In each of the four resulting regions, closed nonzero <contours> surround its extremum; levels closer to zero extend further from the extremum towards the zero-level axes and towards large distance. The height tends to zero at infinity. The figure marks the four extrema and central <saddle point>, and includes the downhill path used below.
\Image[/past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2009/paper-2-gaussian-contours.png]
{title=Contours, stationary points and the steepest downhill path on the Gaussian-weighted surface}
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