The diagram shows the graph of Folium of Descartes with cartesian equation ${{x}^{3}}+{{y}^{3}}=3axy

Question

The diagram shows the graph of Folium of Descartes with cartesian equation ${{x}^{3}}+{{y}^{3}}=3axy$, where a is a positive constant. The curve passes through the origin, and has an oblique asymptote with equation $y=-x-a$. Given that $\left( 0,0 \right)$ is a stationary point on the curve, find, in terms of a, the coordinates of the other stationary point. [5] Sketch the graph of ${{\left| x \right|}^{3}}+{{y}^{3}}=3a\left| x \right|y$, including the equations of any asymptotes, coordinates of the stationary points and the point where the graph crosses the $x$-axis. [3]

Accepted Answer

(i) $(2^{1/3}a, 2^{2/3}a)$

2019 RI P1 Q5

2019 RI P1 Q5

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