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A family of chords is drawn from the origin to the circle (x-1)²+y²=1. The equation of the locus of the midpoints of these chords is:
- x² + y² = 1
- x² + y² = x
- x² + y² = y
- None of these
Correct answer: x² + y² = x
Solution
The locus of the midpoints of the chords drawn from the origin to the circle can be derived using the midpoint formula and the properties of circles. The resulting equation, x² + y² = x, represents a circle that is centered at (0.5, 0) with a radius of 0.5, which accurately describes the midpoints of the chords.
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