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PQ is a double ordinate of the parabola y² = 4ax. The normal at P meets the line through Q parallel to the x-axis at G. The locus of G is a parabola having:
- length of latus rectum equal to 4a
- vertex at (4a, 0)
- directrix as the line x - 3a = 0
- focus at (5a, 0)
Correct answer: length of latus rectum equal to 4a
Solution
Eliminating t from G's coordinates yields a parabola y² = 4a(x - 4a) type form whose latus rectum length equals 4a.
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