The graph of the equation x3 + y3 = 3axy, where a is any nonzero constant, is called the folium of Descartes.
(a) Verify that (0, 0) is a point on this curve.
(b) Obtain a parametrization of the folium by considering the family y = tx of lines through (0, 0) with slopes t and finding, in terms of t, where each of these lines intersects the folium.
(c) Obtain a sketch, by hand or computer, using the parametrization in (b). Conjecture whether the folium has an asymptote.
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