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

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

Find the distance of the point P(-1,-5,-10) from the point of intersection of the line joining the points A(2,-1,2)a n dB(5,3,4) with the plane x-y+z=5.

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

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

Show that the relation R on 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!=(0,\ 0) is the circle passing through P with origin as centre.

Show that the relation R on 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!=(0,\ 0) is the circle passing through P with origin as centre.

If P is any point on the plane l x+m y+n z=pa n dQ is a point on the line O P such that O PdotO Q=p^2 , then find the locus of the point Qdot

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 (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 :