Question

if a ≠b≠o prove that the point (a,a²) (b,b²)and (0,0) will be not collinear​

Answer 1

     

Slope of line formed by points (a, a²) and (b, b²),

$\frac{b^2-a^2}{b-a} = \frac{(b+a)(b-a)}{b-a} = a+b$

Slope of line formed by points (a, a²) and (0, 0),

$\frac{a^2-0}{a-0} = \frac{a^2}{a}=a$

Slope of line formed by points (b, b²) and (0, 0),

(not necessary if two slopes are found)

$\frac{b^2-0}{b-0}=\frac{b^2}{b}=b$

Here we get three different slopes.

∴ Points (0, 0), (a, a²) and (b, b²) are not collinear.

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