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)/(2)a^(2)(t_(1)-t_(2))^(3)

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

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

Tangents to the parabola y^2=4ax at P(at_1^2,2at_1)and Q(at_2^2,2at_2) meet at T. If DeltaPTQ is right - angled at T, then 1/(PS)+1/(QS) is equal to (where , S is the focus of the given parabola)

Find the distance between the points : ( at_1^2 , 2at_1) and (at_2 ^2, 2at_2)

The tangent at P( at^2, 2at ) to the parabola y^(2)=4ax intersects X axis at A and the normal at P meets it at B then area of triangle PAB is

The normals at P,R,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

If P(at_(1)^(2),2at_(1)) and Q(at_(2)^(2),2at_(2)) are the ends of focal chord of the parabola y^(2)=4ax then t_(1)t_(2)