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`

Find the distance of the point P from the line l in that : l: x/a - y/b = 1 and P-= (b, a)

Find the distance of the point P from the line l in that : l: 12x-7=0, P-= (3, -1)

Find the distance of the point P from the line l in that : l:12(x+6)=5 (y-2) and P-=(-3, -4)

Find the distance of the point P from the line l in that : l : 12 (x+6) = 5 (y-2) and P-= (-1, 1)

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

Given equation of line L_1 is y = 4 Write the co-ordinates of point P.

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 P.O Q=p^2 , then find the locus of the point Qdot

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

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