The tangent to the parabola `y^(2)=4ax` at `P(at_(1)^(2), 2at_(1))" and Q"(at_(2)^(2), 2at_(2))` intersect on its axis, them

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)

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 1/2a^2(t_1-t_2)^3

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 1/2a^2(t_1-t_2)^3

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 1/2a^2(t_1-t_2)^3

If the extremities of a focal chord of the parabola y^(2) = 4ax be (at_(1)^(2) , 2at_(1)) and (at_(2)^(2) ,2at_(2)) , show that t_(1)t_(2) = - 1

The normal to the parabola y^(2)=4ax at P(am_(1)^(2),2am_(1)) intersects it again at Q(am_(2)^(2), 2am_(2)) .If A be the vertex of the parabola then show that the area of the triangle APQ is (2a^(2))/(m_(1))(1+m_(1)^(2))(2+m_(1)^(2)) .

The tangents to the parabola y^(2)=4ax at P (t_(1)) and Q (t_(2)) intersect at R. The area of Delta PQR is

If the tangents to the parabola y^(2)=4ax at (x_(1),y_(1)),(x_(2),y_(2)) intersect at (x_(3),y_(3)) then

If a circle intersects the parabola y^(2) = 4ax at points A(at_(1)^(2), 2at_(1)), B(at_(2)^(2), 2at_(2)), C(at_(3)^(2), 2at_(3)), D(at_(4)^(2), 2at_(4)), then t_(1) + t_(2) + t_(3) + t_(4) is