We have,
A(x1,y1)=(a,a2)
B(x2,y2)=(b,b2)
C(x3,y3)=(0,0)
We know that,
Three points are not collinear
If, Areaof triangle≠0
[x1(y2−y3)+x2(y3−y1)+x3(y1−y2)]=0
12[a(b2−0)+b(0−a2)+0(b2−a2)]
=12(ab2−a2b)≠0
It is not collinear.
Hence proved.
If a≠b≠c prove that (a,a2),(b,b2)(0,0) will not be collinear.