If the point `(x_1+t(x_2-x_1),y_1+t(y_2-y_1))` divides the join of `(x_1,y_1)` and `(x_2, y_2)` internally, then `t<0` (b) `01` (d) `t=1`

If the point x_1+t(x_2-x_1),y_1+t(y_2-y_1) divides the join of (x_1,y_1) and (x_2,y_2) internally in ratio of t:1 then vlaue of t is

If the line joining the points (_x_1, y_1) and (x_2, y_2) subtends a right angle at the point (1,1), then x_1 + x_2 + y_2 + y_2 is equal to

If theta\ is the angle which the straight line joining the points (x_1, y_1)a n d\ (x_2, y_2) subtends at the origin, prove that tantheta=(x_2y_1-x_1y_2)/(x_1x_2+y_1y_2)\ a n dcostheta=(x_1x_2+y_1y_2)/(sqrt(x1 2 x2 2+y2 2x1 2+y1 2x2 2+ y1 2y2 2))

If the points P(h , k),\ Q(x_1, y_1)a n d\ R(x_2, y_2) lie on a line. Show that: (h-x_1)(y_2-y_1)=(k-y_1)(x_2-x_1)dot

The ratio in which the line segment joining P(x_1,\ y_1) and Q(x_2,\ y_2) is divided by x-axis is (a) y_1: y_2 (b) y_1: y_2 (c) x_1: x_2 (d) x_1: x_2

If the image of the point (x_1, y_1) with respect to the mirror ax+by+c=0 be (x_2 , y_2) then. (a) (x_2-x_1)/a = (a x_1 + b y_1+ c)/(a^(2)+b^(2)) (b) (x_2-x_1)/a = (y_2 - y_1)/b (c) (x_2-x_1)/a = -2 ((a x_1 + b y_1+ c)/(a^(2)+b^(2))) (d) None of these

If the tangents and normals at the extremities of a focal chord of a parabola intersect at (x_1,y_1) and (x_2,y_2), respectively, then (a) x_1=y_2 (b) x_1=y_1 (c) y_1=y_2 (d) x_2=y_1

Three points A(x_1 , y_1), B (x_2, y_2) and C(x, y) are collinear. Prove that: (x-x_1) (y_2 - y_1) = (x_2 - x_1) (y-y_1) .

If the points (x_1, y_1),(x_2,y_2), and (x_3, y_3) are collinear show that (y_2-y_3)/(x_2x_3)+(y_3-y_1)/(x_3x_1)+(y_1-y_2)/(x_1x_2)=0

If (x_1-x_2)^2+(y_1-y_2)^2=144 ,(x_2-x_3)^2+(y_2-y_3)^2=25 and (x_3-x_1)^2+(y_3-y_1)^2=169 , then the value of |[x_1,y_1, 1],[x_2,y_2 ,1],[x_3,y_3, 1]|^2 is 30 (b) 30^2 (c) 60 (d) 60^2