The points `(a t_1^2, 2 a t_1),(a t_2^2, 2a t_2) and (a ,0)` will be collinear, if

If the points : A(at_(1)^(2),2at_(1)),B(at_(2)^(2),2at_(2)) and C(a,0) are collinear,then t_(1)t_(2) are equal to

The three distinct point A(t_(1)^(2),2t_(1)),B(t_(2)^(2),2t_(2)) and C(0,1) are collinear,if

If the line joining the points (at_1^2,2at_1)(at_2^2, 2at_2) is parallel to y=x then t_1+t_2=

If the points (a,0),(at12,2at_(1)) and at2,2at_(2) ) are collinear,write the value of t_(1)t_(2) .

From a point P (h, k), in general, three normals can be drawn to the parabola y^2= 4ax. If t_1, t_2,t_3 are the parameters associated with the feet of these normals, then t_1, t_2, t_3 are the roots of theequation at at^2+(2a-h)t-k=0. Moreover, from the line x = - a, two perpendicular tangents canbe drawn to the parabola. If the tangents at the feet Q(at_1^2, 2at_1) and R(at_1^2, 2at_2) to the parabola meet on the line x = -a, then t_1, t_2 are the roots of the equation

If t_(1) and t_(2) are roots of the equation t^(2)+lambda t+1=0 where lambda is an arbitrary constant.Then the line joining the points ((at_(1))^(2),2at_(1)) and (a(t_(2))^(2),2at_(2)) always passes through a fixed point then find that point.

Find the distances between the following pairs of points (t_(1)^(2),2t_(1)) and (t,@2,2t_(2),),t_(1) and t_(2) are the roots of x^(2)-2sqrt(3)x+2=0