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 then locus of t is

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)) in the ratio of

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+y1 2x2 2+y2 2))

If the line joining the points (at_1^2,2at_1)(at_2^2, 2at_2) is parallel to y=x then t_1+t_2=

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 y_1: y_2 (b) y_1: y_2 (c) x_1: x_2 (d) x_1: x_2

The equation to the chord joining two points (x_1,y_1) and (x_2,y_2) on the rectangular hyperbola xy=c^2 is: (A) x/(x_1+x_2)+y/(y_1+y_2)=1 (B) x/(x_1-x_2)+y/(y_1-y_2)=1 (C) x/(y_1+y_2)+y/(x_1+x_2)=1 (D) x/(y_1-y_2)+y/(x_1-x_2)=1

If x=(1-t^2)/(1+t^2) and y=(2at)/(1+t^2) , then (dy)/(dx)=

If x=(2t)/(1+t^(2)),y=(1-t^(2))/(1+t^(2))," then "(dy)/(dx)=