A line through the origin intersects x+1,y=2 and x+y=4 in A,B, and C such that OA*OB*OC=8root2. find equation of the line.

let the eq of line y=mx (m is the slope of line)

 A is the point of intersection of line and x=-1

 A =(-1,-m)

B is the intersection of line and y=2

B =(2/m ,2)

C is the intersection of line and x+y=4

C=(4/m+1 ,4m/m+1 )

 OA.0B.OC=8root2...........1

 OA=root1+m^2 ............2

OB=(2/m)root1+m^2..........3

OC=(4/m+1)root1+m^2.......4

after solving we get m=1

 so the eq of line is y=x