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

Step-by-step solution

Homogenise the equation of the given equation of curve To get the equation of the lines joining the origin to points of intersection of curve (i) and line (ii). gathered x^2+y^2+x y+(x+3 y) ( x+y -2 )+ ( x+y -2 )^2=0 x^2+y^2+x y- 1 2 (x^2+4 x y+3 y^2 ) + 1 4 (x^2+2 x y+y^2 )=0 gathered Now, equation of the bisectors of the angle between the pair of straight line (iii) is aligned x^2-y^2 3+1 & = x y -1 x^2+4 x y-y^2 & =0 aligned Hence, option (a) is correct.