The given curve is $$y^2(a+x)=x^2(3a-x).$$
It is given in my book that when we equate the minimum order term of equation to zero, $$a(y^2-3x^2)=0,$$ we get $y=\sqrt{3}x$, $y=-\sqrt{3}x$, which is tangent at origin.
I don't know how do we choose minimum order term of equation?