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

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

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 point of intersection of the tangents to the parabola y^(2)=4ax at the points t_(1) and t_(2) is -

The tangents at three points A,B,C on the parabola y^(2)=4x taken in pairs intersect at the points P,Q,R if triangle_(1),triangle_(2) be the areas of triangle ABC and PQR respectively then

Normal at a point P(a,-2a) intersects the parabola y^(2)=4ax at point Q.If the tangents at P and Q meet at point R if the area of triangle PQR is (4a^(2)(1+m^(2))^(3))/(m^(lambda)). Then find lambda

Consider the circle x^2 + y^2 = 9 and the parabola y^2 = 8x . They intersect at P and Q in first and fourth quadrant respectively. Tangents to the circle at P and Q intersect the x-axis at R and tangents at the parabola at P and Q intersect the x-axis at S. The radius of the circumcircle of the triangle PRS is-