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Let L1 be a straight line through the origin and L2 be the line x + y = 1. If the lengths of the chords (intercepts) cut by the circle x² + y² + x + 3y = 0 on L1 and L2 are equal, then which equation can represent L1?
- x - 7y = 0
- x + y = 0
- x + 7y = 0
- x - y = 0
Correct answer: x - 7y = 0
Solution
Parameterizing L1 as y = m x gives an intercept length |1+3m|/sqrt(1+m²); equating this to the chord length on L2 leads to a quadratic in m whose admissible solution corresponds to slope 1/7, i.e. x - 7y = 0.
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