The combined equation of the bisectors of the angles between the lines joining the origin to the points of intersection of the curve x^2+y^2+x y+x+3 y+1=0 and the line x+y+2=0 is

Step-by-step solution

Given equation: x^2+y^2+x y+x+3 y+1=0 ...(i) and x+y+2=0 x+y -2 =1 ...(ii) Homogenizing (i) with (ii) aligned & x^2+x y+y^2+x(1)+3 y(1)+1(1)^2=0 & x^2+x y+y^2+x ( x+y -2 )+3 y ( x+y -2 )+ ( x+y -2 )^2=0 & 3 x^2-2 x y-y^2=0 aligned Comparing with a x+2 h x y+b y^2=0a=3,2 h=-2, b=-1 Angle bisector is h (x^2-y^2 )=(a-b) x y aligned & -1 (x^2-y^2 )=(3+1) x y & x^2+4 x y-y^2=0 . aligned