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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?
- Its latus rectum is half that of the original parabola
- Its vertex is (1, 0)
- Its directrix is the y-axis
- 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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