[" Any chord "AB" of "y^(2)=4ax" cuts the axis of the parabola at "P," so "],[" that "AP:AB=1:3" where "A(at_(1)^(2),2at_(1)),B(at_(2)^(2),2at_(2))," then "]

The chord AB of the parabola y^(2)=4ax cuts the axis of the parabola at C. If A-=(at_(1)^(2),2at_(1)),B-=(at_(2)^(2),2at_(2)), and AC:AB1:3, then prove that t_(2)+2t_(1)=0

The points (at_(1)^(2),2at_(1)),(at_(2)^(2),2at_(2)) and (a,0) will be collinear,if

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

The tangent to the parabola y^(2)=4ax at P(at_(1)^(2), 2at_(1))" and Q"(at_(2)^(2), 2at_(2)) intersect on its axis, them

The tangent to the parabola y^(2)=4ax at P(at_(1)^(2), 2at_(1))" and Q"(at_(2)^(2), 2at_(2)) intersect on its axis, them

If the extremities of a focal chord of the parabola y^(2) = 4ax be (at_(1)^(2) , 2at_(1)) and (at_(2)^(2) ,2at_(2)) , show that t_(1)t_(2) = - 1

Find the area of that triangle whose vertices are (at_(1)^(2),2at_(1)),(at_(2)^(2),2at_(2))and(at_(3)^(2),2at_(3)).

Find the area of that triangle whose vertices are (at_(1)^(2),2at_(1)),(at_(2)^(2),2at_(2))and(at_(3)^(2),2at_(3)).

Find the slope of a line passing through the following point: (at_(1)^(2),2at_(1)) and (at_(2)^(2),2at_(2))