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Let P be the intersection of the common tangents to the parabola y² = 12x and the hyperbola 8x² - y² = 8. If S and S' are the foci of the hyperbola, with S on the positive x-axis, in what ratio does P divide SS'?
- 5:4
- 14:13
- 2:1
- 13:11
Correct answer: 5:4
Solution
The common tangents are y = +/-2(x + 1)/... meeting at P = (-1, 0); foci at (3, 0) and (-3, 0); P divides SS' (from (3,0) to (-3,0)) so SP: PS' = 4: 2 = 2: 1, but matching computed P = (-1,0): SP = 4, S'P = 2, ratio 2:1.
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