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Consider the three lines: the y-axis, the line y = 2, and the line l*x + m*y = 1, where the point (l, m) lies on the parabola y² = 4x. The locus of the circumcentre of the triangle formed by these three lines is itself a parabola. Which statement about this locus is correct?

1. vertex is (-2, 3/2)
2. vertex is (2, 3/2)
3. Latus rectum = 1/8
4. Latus rectum = 1/16

Correct answer: vertex is (2, 3/2)

Solution

Working out the circumcentre as a function of the parameter and eliminating it gives a parabola with vertex (2, 3/2), so that statement is correct.

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