if the normal at the point ` t_(1)` on the parabola ` y^(2) = 4ax` meets the parabola again in the point ` t_(2)` then prove that ` t_(2) = - ( t_(1) + 2/t_(1))`

If the normal to the parabola y^2=4a x at point t_1 cuts the parabola again at point t_2 , then prove that t_2 2geq8.

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

If the normals at P(t_(1))andQ(t_(2)) on the parabola meet on the same parabola, then

Find the equation of the tangent at t =2 to the parabola y^(2) = 8x .

If the tangents at the points Pa n dQ on the parabola y^2=4a x meet at T ,a n dS is its focus, the prove that S P ,S T ,a n dS Q are in GP.

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) .

The tangent and normal at P(t) , for all real positive t , to the parabola y^2= 4ax meet the axis of the parabola in T and G respectively, then the angle at which the tangent at P to the parabola is inclined to the tangent at P to the circle passing through the points P, T and G is

Find the equations of the tangent and normal to the parabola y^(2)=8x at t=1/2

Find the position of points P(1,3) w.r.t. parabolas y^(2)=4x and x^(2)=8y .