If `t_(1),t_(2) and t_(3)` are distinct, the points `(t_(1)2at_(1)+at_(1)^(3)), (t_(2),2"at"_(2)+"at_(2)^(3)) and (t_(3) ,2at_(3)+at_(3)^(3))`

If t_(1), t_(2) and t_(3) are distinct, the points (t_(1), 2at_(1) +at_(1)^(3)), (t_(2), 2at_(2)+at_(2)^(3)) and (t_(3), 2at_(3)+at_(3)^(3)) are collinear if

If t_(1), t_(2) and t_(3) are distinct, then the points: (t_(1), 2at_(1), at_(1)^(3)), (t_(2), 2at_(2)+at_(2)^(3)) and (t_(3), 2at_(3)+at_(3)^(3)) are colinear if :

If t_1, t_2 and t_3 are distinct, the points (t_1, 2at_1+at_1^3), (t_2,2at_2+at_2^3) and (t_3,2at_3+at_3^3) are collinear if

If t_1,t_2 and t_3 are distinct, the points (t_1, 2at_1 + at_1^3), (t_2, 2at_2 + at_2^3), (t_3, 2at_3 +at_3^3) are collinear then show that t_1+t_2+t_3=0 .

If t_(1)!=t_(2)!=t_(3) are the lines t_(1)x+y=2at_(1)+at_(1)^(3),t_(2)x+y=2at_(2)+at_(2)^(3),t_(3)x+y=2at_(3)+at_(3)^(3) are concurrent then t_(1)+t_(2)+t_(3)=

Find the area of the triangle with verrtices (at_(1)^(2),2at_(1)),(at_(2)^(2),2at_(2))and(at_(3)^(2),2at_(3))