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

If the chord joining the points t_(1) and t_(2) on the parabola y^(2)=4ax subtends a right angle at its vertex then t_(2)=

If the tangents at t_(1) and t_(2) to a parabola y^2=4ax are perpendicular then (t_(1)+t_(2))^(2)-(t_(1)-t_(2))^(2) =

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

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 normals drawn at the points t_(1) and t_(2) on the parabola meet the parabola again at its point t_(3) , then t_(1)t_(2) equals.

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 .

P(t_(1)) and Q(t_(2)) are the point t_(1) and t_(2) on the parabola y^(2)=4ax. The normals at P and Q meet on the parabola.Show that the middle point PQ lies on the parabola y^(2)=2a(x+2a)