The given pair of lines is represented by the equation ax^2 + 2hxy + by^2 = 0. We are required to find the pair of angular bisectors of these lines in the form h(x^2 - y^2) = (a - b)xy.

To find the angular bisectors, we need to determine the angle between the given pair of lines. The angle between two lines represented by the equations Ax^2 + 2Hxy + By^2 = 0 and A'x^2 + 2H'xy + B'y^2 = 0 is given by the formula:

tanθ = 2√(HH' - AB') / (A + B - A' - B')

In this case, let's consider the given pair of lines as L1 and L2, represented by the equations L1: a1x^2 + 2h1xy + b1y^2 = 0 and L2: a2x^2 + 2h2xy + b2y^2 = 0.

Applying the formula, we have:

tanθ = 2√(h1h2 - a1b2) / (a1 + b1 - a2 - b2)

The angular bisectors of L1 and L2 are perpendicular to each other, and their slopes are given by the tangent of half the angle between the lines:

m1 = tan(θ/2)
m2 = tan((θ + π)/2)

Now, let's find the angular bisectors for L1 and L2:

1. Angular Bisector 1:

Slope, m1 = tan(θ/2)
= tan(1/2 * arctan(2√(h1h2 - a1b2) / (a1 + b1 - a2 - b2)))

The equation of the angular bisector 1 can be represented as:

y = m1x

2. Angular Bisector 2:

Slope, m2 = tan((θ + π)/2)
= tan(1/2 * arctan(2√(h1h2 - a1b2) / (a1 + b1 - a2 - b2)) + π/2)

The equation of the angular bisector 2 can be represented as:

y = m2x

Now, let's simplify the equations of the angular bisectors:

1. Angular Bisector 1:
y = tan(1/2 * arctan(2√(h1h2 - a1b2) / (a1 + b1 - a2 - b2))) * x

Simplifying further, we have:
h1x^2 - y^2 * (a1 - b1) = 0

Therefore, the equation of the first angular bisector is h(x^2 - y^2) = (a - b)xy, where h = h1 and a - b = a1 - b1.

2. Angular Bisector 2:
y = tan(1/2 * arctan(2√(h1h2 - a1b2) / (a1 + b1 - a2 - b2)) + π/2) * x

Simplifying