The combined equation of two lines through the origin and making an angle of 45^ with the line 3 x+y=0 , is

Step-by-step solution

Given line 3 x+y=0 slope =-3 Let the slope of required line be m aligned & 45^ = | m+3 1-3 m | & 1= | m+3 1-3 m | & 2 m^2-3 m-2=0...(i) aligned Since the line passes through origin, its equation is y=m x m = y x Substituting the value of m in equation (i), we get aligned & 2 ( y x )^2-3 ( y x )-2=0 & 2 y^2-3 x y-2 x^2=0 & 2 x^2+3 x y-2 y^2=0 aligned