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`.

The normal at t_(1) and t_(2) on the parabola y^(2)=4ax intersect on the curve then t_(1)t_(2)

The normal at any point P(t^(2), 2t) on the parabola y^(2) = 4x meets the curve again at Q, then the area( triangle POQ) in the form of (k)/(|t|) (1 + t^(2)) (2 + t^(2)) . the value of k is

If the normal at(1, 2) on the parabola y^(2)=4x meets the parabola again at the point (t^(2), 2t) then the value of t, is

The normal drawn at a point (at_(1)^(2), 2at_(1)) of the parabola y^(2)=4ax meets on the point (ar_(2)^(2), 2at_(2)) then

The normal drawn at a point (at_(1)^(2),-2at_(1)) of the parabola y^(2)=4ax meets it again in the point (at_(2)^(2),2at_(2)), then t_(2)=t_(1)+(2)/(t_(1))(b)t_(2)=t_(1)-(2)/(t_(1))t_(2)=-t_(1)+(2)/(t_(1))(d)t_(2)=-t_(1)-(2)/(t_(1))