The line `x - b +lambda y = 0` cuts the parabola `y^(2) = 4ax (a gt 0)` at `P(t_(1))` and `Q(t_(2))`. If `b in [2a, 4a]` then range of `t_(1)t_(2)` where `lambda in R` is

The line x - b + lamda. y = 0 cuts the parabola y^2 = 4ax (a>0) at P(t1) & Q(t2). If b in [2a, 4a] then range of t_1t_2 where lamda in R, is

If the normal to the parabola y^(2)=4ax at point t_(1) cuts the parabola again at point t_(2) then prove that t_(2)^(2)>=8

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

If A (t_(1)) " and " B(t_(2)) are points on y^(2) = 4ax , then slope of AB is

If the normal to the parabola y^(2)=4ax at point t_(1) cuts the parabola again at point t_(2) .Then the minimum value of t_(2)^(2) is

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

Tangents drawn to the parabola y^(2)=8x at the points P(t_(1)) and Q(t_(2)) intersect at a point T and normals at P and Q intersect at a point R such that t_(1) and t_(2) are the roots of equation t^(2)+at+2=0;|a|>2sqrt(2) then locus of R is

The tangents to the parabola y^(2)=4ax at P(at_(1)^(2),2at_(1)), and Q(at_(2)^(2),2at_(2)), intersect at R Prove that the area of the triangle PQR is (1)/(2)a^(2)(t_(1)-t_(2))^(3)

If the tangents to the parabola y^(2)=4ax make complementary angles with the axis of the parabola then t_(1),t_(2)=

If A(at_(1)^(2),2at_(1)) and B(t_(2)^(2),2at_(2)) be the two points on the parabola y^(2)=4ax and AB cuts the x -axis at C sucrabola y^(2)=4ax and AC=3:1. show that t_(2)=-2t_(1) and if AB makes an angle of 90^(@) at the vertex,then find the coordinates of A and B.