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 angle between the lines joining the origin to the points of intersection of curve x^(2)+hxy-y^(2)+gx+fy=0 and fx-gy=k is

The angle between the lines joining the origin to the point of intersection of lx+my=1 and x^2+y^2=a^2 is

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 =