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Normals to the parabola x² = 8y are drawn so that pairs of them meet at right angles. The locus of the point of intersection of such perpendicular normals is itself a parabola. Which statement(s) about this locus is/are correct?
- The length of its latus rectum is 2.
- Its focus is at (0, 11/2).
- The equation of its directrix is 2y - 11 = 0.
- Its axis of symmetry is the line y = 0.
Correct answer: The length of its latus rectum is 2.
Solution
Working through the perpendicular-normals condition for x² = 8y produces a parabola whose latus rectum length is 2 (one quarter of the original 8), so that option is correct.
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