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Let L1 be a line through the origin, and let L2 be the line x + y = 1. If the chord cut off by the circle x² + y² − x + 3y = 0 on L1 has the same length as the chord cut off on L2, then which equation can describe L1?
- x + 7y = 0
- x − y = 0
- x − 7y = 0
- Both (a) and (b)
Correct answer: Both (a) and (b)
Solution
Both options (a) and (b) represent lines through the origin that can yield chords of equal length when intersected with the given circle. The specific slopes of these lines allow for the necessary geometric conditions to be met, resulting in equal chord lengths.
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