ABCD is a square with side AB = 2. A point P moves such that its distance from A equals its distance from the line BD. The locus of P meets the line AC at `T_1` and the line through A parallel to BD at `T_2` and `T_3`. The area of the triangle `T_1 T_2 T_3` is :

If a point P moves such that its distance from the point A(1,1) and the line x+y+2 are equal then the locus is

Let ABCD be a square of side length 2 units. C_(2) is the circle through vertices A, B, C, D and C_(1) is the circle touching all the sides of the square ABCD. L is a line through A A line M through A is drawn parallel to BD. Point S moves such that its distances from the line BD and the vertex A are equal. If locus of S cuts. M at T_(2) and T_(3) and AC at T_(1) , then area of DeltaT_(1)T_(2)T_(3) is

ABCD is a square of side length 2 units. C_(1) is the circle touching all the sides of the square ABCD and C_(2) is the circumcircle of square ABCD. L is a fixed line in the same plane and R is fixed point. A line L' through a is drawn parallel to BD. Point S moves scuh that its distances from the line BD and the vertex A are equal. If loucs S cuts L' at T_(2)andT_(3) and AC at T_(1) , then area of DeltaT_(1)T_(2)T_(3) is

ABCD is a square of side length 2 units. C_(1) is the circle touching all the sides of the square ABCD and C_(2) is the circumcircle of square ABCD. L is a fixed line in the same plane and R is fixed point. A line L' through a is drawn parallel to BD. Point S moves scuh that its distances from the line BD and the vertex A are equal. If loucs S cuts L' at T_(2)andT_(3) and AC at T_(1) , then area of DeltaT_(1)T_(2)T_(3) is

If t is parameter then the locus of the point P(t,(1)/(2t)) is _

A point moves along a stright line in such a way that after t seconds its distance from the origin is s=2t^(2)+3t meters. Find the instantaneous velocities at t = 3 and t = 6 seconds.

A body moves in a straight line along x-axis, its distance from the origin is given by the equation x = 8t-3t ^(2). The average velocity in the interval from t =0 to t =4 is