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

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above x-axis at a distance 3/2 from it.

above x-axis at a distance 2/3 from it.

below x-axis at a distance 3/2 from it.

below x-axis at a distance 2/3 from it.

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detailed solution

Correct option is C

Eliminating x, we get2b2+2a2y+3b2+3a2=0⇒ y=−3/2 which is the required line and hence below x-axis at a distance 3/2 from it.

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

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