Question

The line parallel to the x-axis passing through the intersection of the lines \[ ax + 2by + 3b = 0 \quad \text{and} \quad bx - 2ay - 3a = 0 \] 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:

For horizontal lines: \begin{itemize} \item Find y-coordinate of intersection. \item Sign determines above/below x-axis. \end{itemize}

Answer 1

The Correct Option is C