Normals are drawn to the parabola yz =4ax at points A,B.C whose parameters are t1 12 andt, respectively If these normals enclose a triangle PQR, then prove that 군 íts area is-' (11-4) (4-6) (4-11) (t1 +尽t3)2 Also prove that Δ PQR = Δ ABC (11+12+13)2 12) (2

Normals are drawn to the parabola y^(2)=4ax at the points A,B,C whose parameters are t_(1),t_(2) and t_(3) ,respectively.If these normals enclose a triangle PQR,then prove that its area is (a^(2))/(2)(t-t_(2))(t_(2)-t_(3))(t_(3)-t_(1))(t_(1)+t_(2)+t_(3))^(2) Also prove that Delta PQR=Delta ABC(t_(1)+t_(2)+t_(3))^(2)

P and Q are two distinct points on the parabola, y^2 = 4x with parameters t and t_1 respectively. If the normal at P passes through Q , then the minimum value of t_1 ^2 is

y= -2x+12a is a normal to the parabola y^(2)=4ax at the point whose distance from the directrix of the parabola is

IF the normal to the parabola y^2=4ax at point t_1 cuts the parabola again at point t_2 , prove that t_2^2ge8

The normals at P, Q, R on the parabola y^2 = 4ax meet in a point on the line y = c. Prove that the sides of the triangle PQR touch the parabola x^2 = 2cy.

From the point (3 0) 3- normals are drawn to the parabola y^2 = 4x . Feet of these normal are P ,Q ,R then area of triangle PQR 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 t_2 2geq8.

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 normal to the parabola y^2=4a x at point t_1 cuts the parabola again at point t_2 , then prove that (t_2)^2geq8.

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 t_2^2 geq8.