A straight line L through the origin meets the lines x+y=1 and x+y=3 at P and Q respectively. Through P and Q, two straight lines    and   are drawn, parallel to 2x-y=5 and 3x+y=5 respectively. Lines    and   intersect at R. Show that the locus of R, as L varies, is a straight line.

let L :  y = mx

so,  

let point R be R(h,k)

so by given cond.

  and 

eleminate 'm' from both equn & u will have locus of R . . .

let L :  y = mx

so,  

let point R be R(h,k)

so by given cond.

  and 

eleminate 'm' from both equn & u will have locus of R . . .