If the pair of straight lines ax² + 2hxy – ay² = 0 and bx² + 2gxy – by² =0 be such that each bisect the angle between the other , then

hg + ab = 0 ah + bg = 0

h² – ab = 0 ag + bh = 0

Hello student,
The equation of the bisectors of angles between the lines ax² + 2hxy - ay² = 0 is
(x²-y²)/(a-(-a)) = xy/h
or hx² - 2axy – hy² = 0 ….…. (1)
Also, bx² + 2gxy – by² = 0 …. (2)
Therefore, from (1) and (2), by comparing the coefficients, we get
h/b = -2a/2g
So, hg = -ab or hg + ab = 0.