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 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 le d_(1)(P)+d_(2)(P)le4 , is

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 d_(1)(P) " and " d_(2)(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 le d_(1)(P) +d_(2)(P) le 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

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 (x,y) be any point on the parabola y^(2)=4x. Let P be the point that divides the line segment from (0,0) and (x,y) n the ratio 1:3. Then the locus of P is :

Let O(0.0),A(6,0) and B(3,sqrt3) be the vertices of triangle OAB. Let R those points P inside triangle OAB which satisfy d(P, OA) minimum (d(P,OB),d(P,AB) where d(P, OA), d(P, OB) and d(P, AB) represent the distance of P from the sides OA, OB and AFB respectively. If the area of region R is 9 (a -sqrtb) where a and b are coprime, then find the value of (a+ b)