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The folium of descartes is the curve with equation x^3 + y^3 = 3axy where a...

The folium of descartes is the curve with equation x^3 + y^3 = 3axy where a does not equal 0 and is a constant.

a) Show that for any t not equal to 0, 01 the line y=tx intersects the folium at the origin and exactly one other point P. Express the coordinates of P in terms of t to get a parameterization of the folium.

b) Describe the interval of t-values parameterizing the parts of the curve in quadrants I, II, IV.

c) Consider dy/dx as a function of t and find the points with horizontal or vertical tangent.

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