The given equation of lines are, 3x2+2hxy−3y2=0 And 3x2+2hxy−3y2+2x−4y+c=0 The point of intersection of the lines given by ax2+2hxy+by2+2gx+2fy+c=0‌ is ‌(
hf−bg
ab−h2
,
gh−af
ab−h2
) Thus, the point of intersection of the second line is A(x,y)=A(
2h−3
9+h2
,−
h+6
9+h2
) The equation of diagonal of square passes through origin is, y=
h+6
3−2h
x The equation of diagonal of square that does passes through the origin is 2x−4y+c=0 The diagonal are perpendicular if,