The normala at any point `P` `(t^2, 2t)` on the parabola `y^2 = 4x` meets the curve again at `Q`. Prove that the area of `Delta AQP` is `k/|t| (1+t^2) (2+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

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 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

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

Find the angle at which normal at point P(a t^2,2a t) to the parabola meets the parabola again at point Qdot

Find the angle at which normal at point P(a t^2,2a t) to the parabola meets the parabola again at point Qdot

The normal at (a,2a) on y^2 = 4ax meets the curve again at (at^2, 2at) . Then the value of t=

The normal at P(ct,(c )/(t)) to the hyperbola xy=c^2 meets it again at P_1 . The normal at P_1 meets the curve at P_2 =

The normal to the rectangular hyperbola xy = 4 at the point t_1 meets the curve again at the point t_2 Then

Prove that the length of the intercept on the normal at the point P(a t^2,2a t) of the parabola y^2=4a x made by the circle described on the line joining the focus and P as diameter is asqrt(1+t^2) .