The combined equation of the lines passing through the origin making an acute angle with the line y=x is

Step-by-step solution

The required lines are aligned & y= 1+ 1- x and y= 1- 1+ x & (1+ ) y=(1+ x) x and (1+ ) y=(1- ) x & joint equation & 1+ ) x-(1- ) y 1- ) x-(1+ ) y =0 & . (1- 2 ) x^2- (1+ )^2 )+(1- )^2 x y+ (1- ^2 ) y^2=0 & x^2-2 ( 1+ ^2 1- ^2 )^ x y+y^2=0 & x^2- 2 2 x y+y^2=0 & x^2-2 2 a x y+y^2=0 aligned