Show that the lines joining the origin to the points of intersection of the curve `x^2+xy+y^2+3x+3y-2=0` and the straight line `x-y-sqrt2=0`are mutually perpendicular .

Show that the lines joining the origin with the points of intersection of the curve 7x^2-4xy+8y^2+2x-4y-8=0 with the line 3x-y=2 are mutually perpendicular.

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

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.