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Find the y-intercept of the common tangent to the parabolas y² = 32x and x² = 108y.
- -18
- -12
- -9
- -6
Correct answer: -12
Solution
For y² = 32x (a = 8), the tangent is y = mx + 8/m. Imposing tangency with x² = 108y gives m = -2/3, so the y-intercept 8/m = -12.
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