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 the point (x_(1)+t(x_(2)-x_(1)),y_(1)+t(y_(2)-y_(1))) divides the jor (x_(1),y_(1)) and (x_(2),y_(2)) internally,then t 1(d)t=1

X-axis divides the line segment joining (x_(1),y_(1)) and (x_(2),y_(2)) in the ratio

The coordinates of the point which divides the line segment joining the points (x_1;y_1) and (x_2;y_2) internally in the ratio m:n are given by (x=(mx_2+nx_1)/(m+n);y=(my_2+ny_1)/(m+n))

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))

TP and TQ are tangents to y^(2)=4x at (x_(1),y_(1)) and (x_(2),y_(2)) respectively (y_(1),y_(2)>0) .If (x_(1))/(x_(2))=16 ; then locus of T is y^(2)=ax ,then a 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 the chord of contact of tangents from a point (x_(1),y_(1)) to the circle x^(2)+y^(2)=a^(2) touches the circle (x-a)^(2)+y^(2)=a^(2), then the locus of (x_(1),y_(1)) is