To solve this problem, we need to find the equation of the line that bisects the angle between the lines xy = 0. Let's break down the solution into steps:

Step 1: Find the equation of the lines xy = 0:
The equation xy = 0 represents two lines: x = 0 and y = 0. These are the x-axis and y-axis, respectively.

Step 2: Find the angle between the lines xy = 0:
The lines x = 0 and y = 0 intersect at the origin (0, 0). The angle between these lines is 90 degrees or π/2 radians.

Step 3: Find the equation of the line that bisects the angle between the lines xy = 0:
The line that bisects the angle between two lines is perpendicular to both lines and passes through their point of intersection. In this case, the line will be perpendicular to the x-axis and y-axis and will pass through the origin (0, 0).

The equation of a line that passes through the origin is given by y = mx, where m is the slope of the line. Since the line is perpendicular to both the x-axis and y-axis, the slope will be negative reciprocal of the slopes of the x-axis and y-axis.

The slope of the x-axis is 0, and the slope of the y-axis is undefined. Therefore, the slope of the line that bisects the angle between the lines xy = 0 will be 1.

Step 4: Substitute the value of m into the equation (1 - m2)xy - mx2 = 0:
Substituting m = 1 into the equation, we get:
(1 - 12)xy - 1x2 = 0
Simplifying the equation, we get:
(1 - 1)xy - x2 = 0
0xy - x2 = 0
-x2 = 0
This equation is true for all values of x, which means that the line with slope m = 1 satisfies the equation.

Therefore, the correct answer is '1'.