If the Verticesof a triangle are `P(at_1,a/t_1)`,`Q(at_2,a/t_2)`and `R(at_3,a/t_3)`Show that the orthocentre of the triagle lies on `xy = a^2`.

The vertices of a triangle are [at_1t_2, a(t_1+t_2)],[at_2t_3,a(t_2+t_3)],[at_3t_1,a(t_3+t_1)] Find the orthocentre of the triangle.

The vertices of a triangle are [a t_1t_2,a(t_1 +t_2)] , [a t_2t_3,a(t_2 +t_3)] , [a t_3t_1,a(t_3 +t_1)] Then the orthocenter of the triangle is (a) (-a, a(t_1+t_2+t_3)-at_1t_2t_3) (b) (-a, a(t_1+t_2+t_3)+at_1t_2t_3) (c) (a, a(t_1+t_2+t_3)+at_1t_2t_3) (d) (a, a(t_1+t_2+t_3)-at_1t_2t_3)

Let A(ct_(1), (c)/(t_(1))), B(ct_(2),(c)/(t_(2))) and C(ct_(3),(c)/(t_(3))) be the vertices of the triangle ABC. Show that the ortocentre of the triangle lies on xy=c^(2) .

The coordinates of the vertices of a triangle are [at_(1)t_(2),a(t_(1)+t_(2))],[at_(2),t_(3),a(t_(2)+t_(3))] and [at_(3)t_(1),t_(3)+t_(1))] . Find the coordinates of the ortocentre of the triangle.

Using determinant : find the area of the triangle whose vertices are (at_1^2,2at_1),(at_2^2,2at_2) and (at_3^2,2at_3)

If the extremitied 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_1t_2=-1

Prove that the area of the triangle whose vertices are (t ,t-2),(t+2,t+2), and (t+3,t) is independent of tdot

If t_1, t_2 and t_3 are distinct, the points (t_1, 2at_1+at_1^3), (t_2,2at_2+at_2^3) and (t_3,2at_3+at_3^3) are collinear if

A straight line through the vertex P of a triangle P Q R intersects the side Q R at the points S and the cicumcircle of the triangle P Q R at the point Tdot If S is not the center of the circumcircle, then 1/(P S)+1/(S T) 2/(sqrt(Q SxxS R)) 1/(P S)+1/(S T) 4/(Q R)

If t_1,t_2 and t_3 are distinct, the points (t_1, 2at_1 + at_1^3), (t_2, 2at_2 + at_2^3), (t_3, 2at_3 +at_3^3) are collinear then show that t_1+t_2+t_3=0 .