For a point `P` in the plane, let `d_1(P)a n dd_2(P)` be the distances of the point `P` from the lines `x-y=0a n dx+y=0` respectively. The area of the region `R` consisting of all points `P` lying in the first quadrant of the plane and satisfying `2lt=d_1(P)+d_2(P)lt=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

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(x,y),x<=2 in x-y plane moves on path y=|ax-1|+|ax-2|+ax AA alpha in[0,1] If area of region R consisting of all points P lying in the first quadrant of the plane is A when take it's all values alpha in[0,1], then value of (6)/(A) is

Plot the region of the points P (x,y) satisfying |x|+|y| lt 1.

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 the acute angle bisector of the two planes x - 2y - 2z + 1 = 0 and 2x - 3y - 6 + 1= 0 be the plane P. Then which of the following points lies on P ?

Let P be the set of points (x, y) such that x^2 le y le – 2x + 3 . Then area of region bounded by points in set P is

A point P(x,y) moves so that the sum of the distance from P to the coordinate axes is equal to the distance from P to the point A(1,1). The equation of the locus of P in the first quadrant is-