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A variable line L passes through the fixed point (-2, 0) and intersects the unit circle S: x² + y² = 1 at points P and Q. Find the equation of the locus traced by the midpoint of chord PQ as the line L varies.
- (x + 1)² + y² = 1
- x² + (y - 1)² = 1
- (x - 1)² + y² = 1
- x² + (y + 1)² = 1
Correct answer: (x + 1)² + y² = 1
Solution
The perpendicularity condition and the collinearity of M with the fixed point (-2,0) give k² = -h(h+2), which simplifies to (h+1)² + k² = 1. The locus is a circle centred at (-1, 0) with radius 1.
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