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JEE Main 2016 Mathematics question

MathematicsStraight LinesJEE Main 2016

If a variable line drawn through the intersection of the lines and , meets the coordinate axes at A and B, , then the locus of the midpoint of AB is:

Answer: (1)

Solution

First find the fixed point. The lines are and ; adding gives and subtracting gives , so and the point is . Let the variable line meet the axes at and , with midpoint

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Question ID VK-115562