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Find the equation of a line of slope 1 that cuts off chords of equal length on the two circles x² + y² = 4 and x² + y² - 10x - 14y + 65 = 0.
- y = x - 6
- y = x + 6
- y = x - 3
- y = x + 3
Correct answer: y = x - 6
Solution
With both centres giving equal chords, solving r1² - d1² = r2² - d2² for the line y = x + c yields c = -6, i.e. the line y = x - 6.
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