The normal at a point `t_1` on `y^2 = 4ax` meets the parabola again in the point `t_2`. Then prove that `t_1 t_2 + t_1^2 + 2=0`

The normal at a point (bt_1^(2) , 2bt_1) on a parabola meets the parabola again in the point (bt_2^(2) , 2bt_2) then

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 to y^(2) =4ax at t_1 cuts the parabola again at t_2 then

If the normal at the point t_(1) to the rectangle hyperola xy=c^(2) meets it again at the point t_(2) prove that t_(1)^(3) t_(2)=-1

If the normal at t_(1) on the parabola y^(2)=4ax meet it again at t_(2) on the curve then t_(1)(t_(1)+t_(2))+2 =