Consider two lines `L_(1) " and " L_(2)` given by x-y=0 and x+y=0, respectively, and a moving point P(x,y). Let d`(P,L_(i))`, i=1,2, represents the distance of point P from the line ` L_(i)`. If point P moves in a certain region R is such a way that `2 le d(P,L_(1))+d(P,L_(2))le 4,`
find the area of region R.

Consider two lines L_1a n dL_2 given by x-y=0 and x+y=0 , respectively, and a moving point P(x , y)dot Let d(P , L_1),i=1,2, represents the distance of point P from the line L_idot If point P moves in a certain region R in such a way that 2lt=d(P , L_1)+d(P , L_2)lt=4 , find the area of region Rdot

Consider the lines L_(1) -=3x-4y+2=0 " and " L_(2)-=3y-4x-5=0. Now, choose the correct statement(s).

Consider two lines L_1a n dL_2 given by a_1x+b_1y+c_1=0a n da_2x+b_2y+c_2=0 respectively where c1 and c2 !=0, intersecting at point PdotA line L_3 is drawn through the origin meeting the lines L_1a n dL_2 at Aa n dB , respectively, such that PA=P B . Similarly, one more line L_4 is drawn through the origin meeting the lines L_1a n dL_2 at A_1a n dB_2, respectively, such that P A_1=P B_1dot Obtain the combined equation of lines L_3a n dL_4dot

Consider the lines given by L_(1):x+3y-5=0 L_(2):3x-ky-1=0 L_(3):5x+2y-12=0 Match the following lists.

Consider the line L 1 : x 1 y 2 z 1 312 +++ ==, L2 : x2y2z3 123

Consider the line L 1 : x 1 y 2 z 1 312 +++ ==, L2 : x2y2z3 123

Show that the distance of the point P from the line l with equation vec(r)=vec(a)+vec(tb) is given by (|vec(b)xxvec(PQ)|)/(|vec(b)|) , where Q is any point on line l.

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

P is a point on the straight line 7x-4y-29=0 . If the foot of the perpendicular drawn from P on the line 5x+2y+18=0 be N(-2,-4) , find the coordinates of P.

Let L_(1) be a striaght line passing through the origin and L_(2) be the straight x+y=1 . If the intercepts made by the circle x^(2)+y^(2)-x+3y=0 on L_(1) and L_(2) are equal, find the equation of the line L_(1) .