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TP and TQ are tangents to the parabola y² = 4x, and the normals at P and Q meet at a point R lying on the parabola. The locus of the centre of the circle circumscribing triangle TPQ is itself a parabola. Which of the following is a correct property of that locus parabola?
- foot of directrix is (7/8, 0)
- vertex is (1, 0)
- length of latus-rectum is 1/4
- focus is (9/8, 0)
Correct answer: foot of directrix is (7/8, 0)
Solution
Working out the circumcentre of triangle TPQ under the given normal-intersection constraint yields a parabola whose foot of directrix is (7/8, 0).
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