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)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

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 distance of a point P from the striaght line x=-4 is equal to its distance from the point (3,0) . Find the equation to the locus of P.

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.

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 P be the point (1, 0) and Q be a point on the locus y^2= 8x . The locus of the midpoint of PQ is

Let P be the point (1,0) and Q be a point on the locus y^(2)=8x . The locus of the midpoint of PQ is

Plot the region of the points P(x,y) satisfying 2 gt max. {|x|, |y|}.

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?

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.