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P lies on the parabola y² = 4ax (a > 0) with vertex A. Line PA is extended to meet the directrix at D, and M is the foot of the perpendicular from P to the directrix. A circle drawn with MD as diameter cuts the x-axis at a point with coordinates:
- (-a, 0)
- (-3a, 0)
- (-2a, 0)
- (a, 0)
Correct answer: (-a, 0)
Solution
Both M and D have x = -a (they lie on the directrix), so the circle on MD as diameter meets the x-axis exactly where the directrix crosses it, namely (-a, 0).
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