For a point `P` in the `XY` plane.Let `d_(1)(p),d_(2)(p)` and `d_(3)(p)` be the distances of the point `P` from the `x` axis,`y` axis and `x-y=0` respectively. If `A` is area of the region `R` consisting of all points `P` lying in the XY plane and satisfying `d_(1)(P)+d_(2)(P)+sqrt(2)d_(3)(P)=5` then Which of the following is/are CORRECT

For a point P in the plane,let d_(1)(P) and d_(2)(P) be the distances of the point P from the lines x-y=0 and x+y=0 respectively.The area of the region R consisting of all points P lying in the first quadrant of the plane and satisfying 2<=d_(1)(P)+d_(2)(P)<=4, is

For a point P in the plane, let d1 (P) and d2 (P) be the distance of the point P from the lines x – y = 0 and x + y = 0 respectively. The area of the region R consisting of all points P lying in the first quadrant of the plane and satisfying 2 < d1(P) + d2 (P)< 4, is

Write the distance of the point P(2,3,5) from the xy-plane.

The point P is on the y -axis.If P is equidistant from (1,2,3) and (2,3,4) then P is

Consider a rectangle ABCD formed by the points A=(0,0), B= (6, 0), C =(6, 4) and D =(0,4), P (x, y) is a moving interior point of the rectangle, moving in such a way that d (P, AB)le min {d (P, BC), d (P, CD) and d (P, AD)} here d (P, AB), d (P, BC), d (P, CD) and d (P, AD) represent the distance of the point P from the sides AB, BC, CD and AD respectively. Area of the region representing all possible positions of the point P is equal to

Let d(P, OA) le min {d (P, AB), d(P, BC), d (P, OC)} where d denotes the distance from the point to the corresponding line and S be the region consisting of all those points P inside the rectangle OABC such that O = (0, 0), A = (3, 0), B = (3, 2) and C = (0, 2), which satisfy the above relation, then area of the region S is

Let ABC be a triangle with vertices A-=(6,2sqrt(3)+1)) ) B-=(4,2) and C-=(8,2). Let R be the region consisting of all those points P inside Delta ABC which satisfyd (P,BC)>=max{d(P,AB);d(P,AC)}, where d(P,L) denotes the distance of the point from the line L,then

Let O(0,0),A(2,0),a n dB(1 1/(sqrt(3))) be the vertices of a triangle. Let R be the region consisting of all those points P inside O A B which satisfy d(P , O A)lt=min[d(p ,O B),d(P ,A B)] , where d denotes the distance from the point to the corresponding line. Sketch the region R and find its area.

The point P is on the y -axis. If P is equidistant from (1,2,3) and (2,3,4) then P_(y) is