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.

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 .

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 equation to the pair of lines joining the origin to the points of intersection of the curve 7x^(2)-4xy+8y^(2)+2x-4y-8=0 with the striaht line 3x-y=2 and the angle between them.

If the straight lines joining the origion with the points of intersection of the curve 3x^2-xy+3y^2+2x-3y+4=0 & the line 2x+3y=k are perpendicular then prove that 6k^2-5k+52=0 .

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.