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: - Mathematics MCQ AIEEE 2026 | ExamTest.live

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The line parallel to the x-axis and 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:

Solution & Step-by-step Explanation

To find the intersection point (x, y), solve the system: a x + 2 b y = - 3 b b x - 2 a y = 3 a Multiply (1) by b and (2) by a : ab x + 2 b^{2} y = - 3 b^{2} ab x - 2 a^{2} y = 3 a^{2} Subtracting the two equations: (2 b^{2} + 2 a^{2}) y = - 3 b^{2} - 3 a^{2} 2 (a^{2} + b^{2}) y = - 3 (a^{2} + b^{2}) Since (a, b) \neq = (0, 0), a^{2} + b^{2} \neq = 0 : y = - 3/2 .The line parallel to the x-axis passing through the intersection must have the equation y = constant .Thus, the equation is y = - 3/2 .This line is 3/2 units below the x-axis.

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The line parallel to the x-axis and 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:

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

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

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

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

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