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A circle is centred at the focus of the parabola y² = 2px and is tangent to the parabola's directrix. Find a point where this circle intersects the parabola.

1. (p/2, p)
2. (p/2, -p)
3. (-p/2, p)
4. (-p/2, -p)

Correct answer: (p/2, p)

Solution

The circle (x - p/2)² + y² = p² meets y² = 2px at x = p/2, giving y = +/-p, e.g. (p/2, p).

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