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

1. below the x-axis at a distance of 3/2 from it
2. below the x-axis at a distance of 2/3 from it
3. above the x-axis at a distance of 3/2 from it
4. above the x-axis at a distance of 2/3 from it

Correct answer: below the x-axis at a distance of 3/2 from it

Solution

Solving ax+2by+3b=0 and bx-2ay-3a=0 gives the intersection (0, -3/2). The line through it parallel to the x-axis is y = -3/2, which lies below the x-axis at a distance 3/2 from it.

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