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 :

A point P moves so that its distance from the line given by x=-3 is equal to its distance from the point (3, 0). Show that the locus of P is y^(2)=12x .

A point moves so that square of its distance from the point (3,-2) is numerically equal to its distance from the line 5x-12y=3 . The equation of its locus is ..........

A point moves so that square of its distance from the point (3,-2) is numerically equal to its distance from the line 5x-12y=3 . The equation of its locus 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

A particle moves in a straight line such that its distance in 't' seconds from a fixed point is (6t-t^(2)) cm. find its velocity at the end of t=2 sec.

Two planets are at distance R_1 and R_2 from the Sun. Their periods are T_1 and T_2 then (T_1/T_2)^2 is equal to

The reflection of the point (t - 1,2t+ 2) in a line is (2t + 1,t) , then the equation of the line has slope equals to

If a point is moving in a line so that its velocity at time t is proportional to the square of the distance covered, then its acceleration at time t varies as

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 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