The normal at `t_(1)` on the parabola meets again at `t_(2)` then find relation between `t_(1)` and `t_(2)`

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

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

Normal at P(t1) cuts the parabola at Q(t2) then relation

STATEMENT-1 : If normal at ends of double ordinate x = 4 of parabola y^(2) =4x meet the curve again at P and P' respectively, then PP' = 12 units. and STATEMENT-2 : If normal at t_(1) of y^(2) =4ax met parabola again at t_(2) , then t_(2) = -t_(1) -(2)/(t_(1)) .

A projectille can have the same range R for two angles of projection. If t_(1) and t_(2) be the time of flight in the two cases, then find the relation between t_(1), t_(2) and R .

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.

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

A mass is suspended separately by two springs and the time periods in the two cases are T_(1) and T_(2) . Now the same mass is connected in parallel (K = K_(1) + K_(2)) with the springs and the time is suppose T_(P) . Similarly time period in series is T_(S) , then find the relation between T_(1),T_(2) and T_(P) in the first case and T_(1),T_(2) and T_(S) in the second case.

Normals drawn to the hyperbola xy=2 at the point P(t_1) meets the hyperbola again at Q(t_2) , then minimum distance between the point P and Q is