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Question

If ab0, prove that the points (a,a2),(b,b2) and (0,0) will not be collinear.

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Solution

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 triangle0

[x1(y2y3)+x2(y3y1)+x3(y1y2)]=0

12[a(b20)+b(0a2)+0(b2a2)]

=12(ab2a2b)0


It is not collinear.

Hence proved.


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