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A point divides, internally in the ratio 1: 2, the segment joining (0, -1) to a variable point lying on the parabola x² = 4y. Find the locus of the dividing point.

1. 9x² - 12y = 8
2. 9x² - 3y = 2
3. x² - 3y = 2
4. 4x² - 3y = 2

Correct answer: 9x² - 12y = 8

Solution

Using the section formula and eliminating the parameter t gives the locus 9x² - 12y = 8.

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