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Three distinct points on the parabola y = x² are chosen so that the normal lines drawn at these points all pass through one common point (a, b). What is the sum of the x-coordinates of these three points?
- 0
- (2b - 1)/2
- a/2
- a + b
Correct answer: 0
Solution
Setting up the normal condition produces a cubic in t whose coefficient of t² is zero, so the roots sum to zero.
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