Folium of Descartes :-
cube of x + cube of y = 3axy
It is symmetrical about the line
y=x
and meets in at the point
(3a/2, 3a/2)
It passes through the origin and
x=0 y=0
are the tangents there so that the origin is a node on the curve.
It meets the co-ordinate axes at the origin only.
x+y+a=0 is its only asymptote.
x, y can not both be negative .
So, that no part of the curve lies in the third quadrant.
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