Folium of Descartes :-
cube of x + cube of y = 3axy
It is symmetrical about the line
and meets in at the point
It passes through the origin and
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.