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The locus of the points of trisection of all double ordinates of the parabola y² = l*x is itself a parabola. Find the length of its latus rectum.

1. l/9
2. 2l/9
3. 4l/9
4. l/36

Correct answer: l/9

Solution

With Y = y/3, y = 3Y; substituting in y² = l*x gives 9Y² = l*X, i.e. Y² = (l/9)X, latus rectum l/9.

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