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From the vertex of the parabola y² = 4ax, perpendicular chords are drawn. Find the locus of the centre of the circle that passes through the vertex and through the mid-points of these two perpendicular chords.

1. a parabola with latus rectum a/2
2. a parabola with vertex (-a, a)
3. a parabola with latus rectum a
4. a parabola with vertex (2a, 0)

Correct answer: a parabola with latus rectum a/2

Solution

Working through the geometry, the locus of the circle's centre is itself a parabola whose latus rectum is a/2.

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