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From the vertex of the parabola y² = 4ax, two chords are drawn perpendicular to each other. Using these chords as adjacent sides, a rectangle is completed. What is the locus of the rectangle's vertex opposite to the parabola's vertex?

1. an equal (congruent) parabola
2. a parabola with focus at (9, 0)
3. a parabola with directrix x - 7 = 0
4. a parabola with vertex-tangent x = 8

Correct answer: an equal (congruent) parabola

Solution

With perpendicular vertex chords, t1 t2 = -4; the far vertex of the rectangle traces a parabola congruent to the original (same 4a), shifted along the axis.

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