`A=(sqrt(1-t^2)+t, 0)` and `B=(sqrt(1-t^2)-t, 2t)` are two variable points then the locus of mid-point of `AB` is

Locus of the middle points of the line segment joining P(0, sqrt(1-t^2) + t) and Q(2t, sqrt(1-t^2) - t) cuts an intercept of length a on the line x+y=1 , then a = (A) 1/sqrt(2) (B) sqrt(2) (C) 2 (D) none of these

If the coordinates of a vartiable point P be (t+(1)/(t), t-(1)/(t)) , where t is the variable quantity, then the locus of P is

If P(1+t/(sqrt(2)),2+t/sqrt(2)) is any point on a line, then the range of the values of t for which the point P lies between the parallel lines x+2y=1a n d2x+4y=15. is (a) (4sqrt(2))/3lttlt5(sqrt(2)) 6 (b) 0lttlt(5sqrt(2)) (c) 4sqrt(2)lttlt0 (d) none of these

(-1)/(2)int(dt)/(sqrt(1-t)sqrt(t))

If e^x=(sqrt(1+t)-sqrt(1-t))/(sqrt(1+t)+sqrt(1-t))a and tany/2=sqrt((1-t)/(1+t)) ,then (dy)/(dx) at t=1/2 is (a) -1/2 (b) 1/2 (c) 0 (d) none of these

Let z=t^2-1+sqrt(t^4-t^2),where t in R is a parameter. Find the locus of z depending upon t , and draw the locus of z in the Argand plane.

Find the locus of a variable point (at^2, 2at) where t is the parameter.

If A(at^2, 2at), B((a)/(t^2) , - (2a)/(t)) and C(a, 0) be any three points, show that 1/(AC) + 1/(BC) is independent of t .

A, B, C are respectively the points (1,2), (4, 2), (4, 5). If T_(1), T_(2) are the points of trisection of the line segment BC, the area of the Triangle A T_(1) T_(2) is

If the points (0,0), (1,0), (0,1) and (t, t) are concyclic, then t is equal to