Example
Ex:
Find the combined equation of the pair of bisectors of the angles between the pair of straight lines represented by 6x
2
+ 11xy + 3y
2
= 0.
Sol:
Comparing the given equation with ax
2
+ 2hxy + by
2
= 0,
we get a = 6, b = 3, h = 11/2
∴ The equation of the pair of bisectors of the angles between the given pair of lines is
h(x
2
– y
2
) = (a – b)xy
(11/2)(x
2
– y
2
) = (6 – 3)xy
∴ 11(x
2
– y
2
) – 6xy = 0