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

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

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)

The point P lies on 3rd quadrant and its distances from x- axis and y -axis are 6 and 4 respectively . The coordinates of P will be -

Show that the relation R in the set A of points in a plane given by R = {(P,Q): distance of the point P from the origin is same as the distance of the point Q from the origin}, is an equivalence relation. Further, show that the set of all points related to a point P ne (0,0) is the circle passing through P with origin as centre.

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

Find the coordinates of the foot of the perpendicular drawn from the point P(1,-2) on the line y = 2x +1. Also, find the image of P in the line.

If p_1 and p_2 are the lengths of the perpendiculars from the point (2,3,4) and (1,1,4) respectively from the plane 3x-6y+2z+11=0, then for which equation p_1 and p_2 will be the roots?

P is a point on the line y+2x=1, and Qa n dR two points on the line 3y+6x=6 such that triangle P Q R is an equilateral triangle. The length of the side of the triangle is

If sum of the perpendicular distances of a variable point P(x, y) from the lines x + y - 5 = 0 " and " 3x - 2y + 6 = 0 is always 10. Show that P must move on a line.