Question

The line parallel to the x-axis passing through the intersection of the lines \( ax + 2by + 3b = 0 \) and \( bx - 2ay - 3a = 0 \) where \( (a, b) \neq (0, 0) \) is:

• A. above x-axis at a distance \( \frac{3}{2} \) from it.
• B. above x-axis at a distance \( \frac{2}{3} \) from it.
• C. below x-axis at a distance \( \frac{3}{2} \) from it.
• D. below x-axis at a distance \( \frac{2}{3} \) from it.

Hint:

When solving for the intersection of two lines, be careful about potential cases where coefficients might be zero. However, in this problem, the condition \( (a, b) \neq (0, 0) \) ensures that we don't have trivial cases where both \( a \) and \( b \) are zero simultaneously.