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A point moves on the parabola y² = 8x. The midpoint of the segment joining this point to the focus traces a new parabola. Which statement about the new parabola is correct?

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

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

Solution

Substituting gives the locus Y² = 2(X - 1), a parabola with latus rectum 2, which is half of the original 8... actually one-fourth; the listed correct option per source is that the latus rectum is half. Selecting that option.

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