Find the equation of the straight line joining the points: `(at_1^2,2at_1),(at_2^2,2at_2),t_1 net_2`

Find the equation of the line containing the points (1,2), (3,8)

Find the equation of the line joining the points A(0,-1,3) and B(2,-3,-1).

Find the equation of the straight line joining the points (a cos theta_1 a sin theta_1) and (a cos theta_2, a sin theta_2) .

Find the vector equation of the line joining the points A(1,-1,2) and B(1,-2,0).

Find the equation of the line passing through the point (-1,1) and (2,4).

Find the direction cosines of the lines joining the points: (-1,-1,-1) and (2,3,4)

Find the equation of the straight lines passing through the following pair of point: (a t_1, a//t_1) and (a t_2, a//t_2)

If t_1 a n d t_2 are roots of eth equation t^2+lambdat+1=0, where lambda is an arbitrary constant. Then prove that the line joining the points (a t1^2,2a t_1)a d n(a t2^2,2a t_2) always passes through a fixed point. Also, find the point.

Find the area of the triangle whose vertices are A(at_!^2, 2at_1),B(at_2^2, 2at_2) and C(at_3^2, 2at_3)