If `A(at_1^2, 2at_1)` and `B(t_2^2,2at_2)` be the two points on the parabola `y^2 = 4ax` and AB cuts the x-axis at C such that `AB : AC = 3: 1`. show that `t_2 = -2t_1` and if AB makes an angle of `90^@` at the vertex, then find the coordinates of A and B.

If A(at_(1)^(2),2at_(1)) and B(t_(2)^(2),2at_(2)) be the two points on the parabola y^(2)=4ax and AB cuts the x -axis at C sucrabola y^(2)=4ax and AC=3:1. show that t_(2)=-2t_(1) and if AB makes an angle of 90^(@) at the vertex,then find the coordinates of A and B.

Let P(at_(1)^(2),2at_(1)) and Q(at_(2)^(@),2at_(2)) are two points on the parabola y^(2)=4ax Then,the equation of chord is y(t_(1)+t_(2))=2x+2at_(1)t_(2)

If 't_1' and 't_2' be the ends of a focal chord of the parabola y^2=4ax then t_1t_2 is equal to

Show that the normal at a point (at^2_1, 2at_1) on the parabola y^2 = 4ax cuts the curve again at the point whose parameter t_2 = -t_1 - 2/t_1 .

IF the normal to the parabola y^2=4ax at point t_1 cuts the parabola again at point t_2 , prove that t_2^2ge8