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P is a point on the parabola y² = 4ax (a > 0) with vertex A. PA produced meets the directrix at D, and M is the foot of the perpendicular from P to the directrix. A circle is drawn with MD as diameter. Find the coordinates of the point where this circle meets the x-axis.

1. (-3a, 0)
2. (-a, 0)
3. (-2a, 0)
4. (a, 0)

Correct answer: (-a, 0)

Solution

Line AP meets x = -a at D = (-a, -2a/t); the circle on MD as diameter meets the x-axis exactly at the focus's mirror... it passes through (-a, 0) on the directrix.

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