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A point P moves on the parabola y² = 4ax. The mid-point of the focal radius SP (S being the focus) traces another parabola. Which one of the following statements about this locus is correct?

1. Its latus rectum is half the latus rectum of the original parabola
2. Its vertex is at (a/2, 0)
3. Its directrix is the y-axis
4. Its focus is at (a, 0)

Correct answer: Its latus rectum is half the latus rectum of the original parabola

Solution

Eliminating t gives Y² = 2a(X - a/2), a parabola with latus rectum 2a, which is half of the original 4a.

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