Find the angle between the lines joining the origin to the points of intersection of the curve `x^2+2xy+y^2+2x+2y-5=0` and the line 3x-y+1=0.

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

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

Find the values of k ,if the lines joining the origin to the points of intersection of the curve 2x^(2)-2xy+3y^(2)+2x-y-1=0 and the line x+2y=k are mutually perpendicular.

If theta is the angle between the lines joining the origin to the points of intersection of the curve 2x^2+3y^2=6 and the line x+y =1, then sin theta =