If the angle between the lines represented by `ax^(2) + 2hxy + by^(2) = 0` is equal to the angle between the lines `2x^(2) - 5xy + 3y^(2) = 0`, then show that `100(h^(2)-ab) = (a+b)^(2)`.

Explanation

To solve the problem, we need to show that if the angle between the lines represented by the equations \( ax^2 + 2hxy + by^2 = 0 \) and \( 2x^2 - 5xy + 3y^2 = 0 \) are equal, then the equation \( 100(h^2 - ab) = (a + b)^2 \) holds true.

### Step-by-Step Solution:

1. **Identify the angles between the lines**:
The angle \( \theta \) between the lines represented by the equation \( ax^2 + 2hxy + by^2 = 0 \) can be given by the formula:
\[
\tan \theta = \frac{2\sqrt{h^2 - ab}}{a + b}
...