Find the coordinates o the vertices of a triangle, the equations of whose sides are: `y(t_1+t_2)=2x+2a t_1a t_2,\ y(t_2+t_3)=2x+2a t_2t_3\ a n d\ , y(t_3+t_1)=2x+2a t_1t_3dot`

If the points (a ,0),(a t1 ^ 2,\ 2a t_1)a n d\ a t2^ 2,\ 2a t_2) are collinear, write the value of t_1t_2dot

Find the equations of the tangent and the normal to the curve x=a t^2,\ \ y=2a t at t=1 .

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

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

Find the equation of tangent to the curve by x = t^(2) + t + 1 , y = t^(2) - t + 1 at a point where t = 1

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

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

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

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) + a(t_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)

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)