What is the condition for the points (a, 0),( | vedclass

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(C) Points are collinear if the area of the triangle formed by them is zero.Area $= \frac{1}{2} |x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)| = 0

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$t_1t_2 = -1$

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(C) Points are collinear if the area of the triangle formed by them is zero.Area $= \frac{1}{2} |x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)| = 0$.Substituting the points $(a, 0)$,$(at_1^2, 2at_1)$,and $(at_2^2, 2at_2)$:$\frac{1}{2} |a(2at_1 - 2at_2) + at_1^2(2at_2 - 0) + at_2^2(0 - 2at_1)| = 0$.Dividing by $2a^2$ (assuming $a 
eq 0$):$|(t_1 - t_2) + t_1^2 t_2 - t_2^2 t_1| = 0$.$t_1 - t_2 + t_1 t_2 (t_1 - t_2) = 0$.$(t_1 - t_2)(1 + t_1 t_2) = 0$.Since $t_1 
eq t_2$ for distinct points,we must have $1 + t_1 t_2 = 0$,which implies $t_1 t_2 = -1$.

What is the condition for the points $(a, 0)$,$(at_1^2, 2at_1)$,and $(at_2^2, 2at_2)$ to be collinear?

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