If points `(t ,\ 2t),\ (-2,\ 6)` and `(3,\ 1)` are collinear, then `t=` (a) `3/4` (b) `4/3` (c) `5/3` (d) `3/5`

If points (1,\ 2),\ (-5,\ 6) and (a ,\ -2) are collinear, then a= (a) -3 (b) 7 (c) 2 (d) -2

Show that the points A(1,3,2),B(-2,0,1) and C(4,6,3) are collinear.

Show that the points A (2, 3, 4), B (3, 4, 6) and C (5, 6, 16) are collinear.

Show that the point A(1,-1,3), B(2,-4,5) and C(5,-13,11) are collinear.

If the points (2,0)(3,2)(5,4) and (0,t) are concylic, show that t=2 or 17.

If the points (2, 3), (0, 2), (4, 5) and (0, t) are concyclic, then t^(3) + 17 is equal to __________.

Show that the point A (1,-1,3), B ( 2,-4,5) and C ( 5,-13,11) are collinear.

Find the value of k if the points A(2,\ 3),\ B(4,\ k)\ a n d\ C(6,\ 3) are collinear.

Show that the points A(-1,\ 4,\ -3),\ B(3,\ 2,\ -5),\ C(-3,\ 8,\ -5)a n d\ D(-3,\ 2,\ 1) are coplanar.

Statement 1 : If a circle S=0 intersects a hyperbola x y=4 at four points, three of them being (2, 2), (4, 1) and (6,2/3), then the coordinates of the fourth point are (1/4,16) . Statement 2 : If a circle S=0 intersects a hyperbola x y=c^2 at t_1,t_2,t_3, and t_3 then t_1-t_2-t_3-t_4=1