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 , P_1)+d(P , L_1)lt=4` , find the area of region `Rdot`

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

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: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

Consider the lines L_1 and L_2 defined by L_1:xsqrt2+y-1=0 and L_2:xsqrt2-y+1=0 For a fixed constant lambda , let C be the locus of a point P such that the product of the distance of P from L_1 and the distance of P from L_2 is lambda^2 . The line y=2x+1 meets C at two points R and S, where the distance between R and S is sqrt(270) . Let the perpendicular bisector of RS meet C at two distinct points R' and S' . Let D be the square of the distance between R' and S'. The value of D is

Consider the lines L_1 and L_2 defined by L_1:xsqrt2+y-1=0 and L_2:xsqrt2-y+1=0 For a fixed constant lambda , let C be the locus of a point P such that the product of the distance of P from L_1 and the distance of P from L_2 is lambda^2 . The line y=2x+1 meets C at two points R and S, where the distance between R and S is sqrt(270) . Let the perpendicular bisector of RS meet C at two distinct points R' and S' . Let D be the square of the distance between R' and S'. The value of lambda^2 is

Consider the bisector (L=0) of the angle between the lines x+2y-11 = 0 and 3x – 6y-5= 0 (the region) which contains the point A(1, -3) . Let P(a,1) and Q(b,2) be two points lying on this line (L=0) . Then

Find the image of the point p wrt the plane L where P-=(1,2,3) and L=2x+2y+4z=38