Chord AC of parabola `y^2 = 4x` subtend `pi/2` at points B & D on the parabola. If A, B, C, D are represented by t1, t2, t3, t4, then

The chord AC of the parabola y^(2)=4ax subtends an angle of 90^(@) at points B and D on the parabola. If points A, B, C and D are represented by (at_(i)^(2), 2at_(i)), i=1,2,3,4 respectively, then find the value of |(t_(2)+t_(4))/(t_(1)+t_(3))| .

The chord A B of the parabola y^2=4a x cuts the axis of the parabola at Cdot If A-=(a t_1^ 2,2a t_1),B-=(a t_2^2,2a t_2) , and A C : A B=1:3, then prove that t_2+2t_1=0 .

The chord A B of the parabola y^2=4a x cuts the axis of the parabola at Cdot If A-=(a t_1 ^2,2a t_1),B-=(a t_2 ^2,2a t_2) , and A C : A B 1:3, then prove that t_2+2t_1=0 .

The chord A B of the parabola y^2=4a x cuts the axis of the parabola at Cdot If A-=(a t_1^ 2,2a t_1),B-=(a t_2^2,2a t_2) , and A C : A B=1:3, then prove that t_2+2t_1=0 .

A circle drawn on any focal AB of the parabola y^(2)=4ax as diameter cute the parabola again at C and D. If the parameters of the points A, B, C, D be t_(1), t_(2), t_(3)" and "t_(4) respectively, then the value of t_(3),t_(4) , is

A circle drawn on any focal AB of the parabola y^(2)=4ax as diameter cute the parabola again at C and D. If the parameters of the points A, B, C, D be t_(1), t_(2), t_(3)" and "t_(4) respectively, then the value of t_(3),t_(4) , is

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 t2 2geq8.