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 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.

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.

[" *** 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."]