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 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)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

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

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 (a) 8 sq. units (b) 4 sq. units (c) 12 sq. units (d) 6 sq. units

A point P(x,y) moves that the sum of its distance from the lines 2x-y-3=0 and x+3y+4=0 is 7. The area bounded by locus P is (in sq. unit)

Let P be the image of the point (3, 1, 7) with respect to the plane x-y+z=3 . Then, the equation of the plane passing through P and containing the straight line (x)/(1)=(y)/(2)=(z)/(1) is

Let there are three points A (0, 4/3), B(–1, 0) and C(1, 0) in x – y plane. The distance from a variable point P to the line BC is the geometic mean of the distances from this point to lines AB and AC then locus of P can be

A line through point A(1,3) and parallel to the line x-y+1 = 0 meets the line 2x-3y + 9 = 0 at point P. Find distance AP without finding point P.

If the point of intersection of the plane 4x - 5y + 2z - 6 = 0 with the line through the origin and perpendicular to the plane x- 2y - 4z = 4 is P, then the distance of the point P from (1, 2,3) is

P is a variable point on the curve y= f(x) and A is a fixed point in the plane not lying on the curve. If PA^(2) is minimum, then the angle between PA and the tangent at P is