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A circle passes through the focus of the parabola x² = 4y and touches the parabola at the point (6, 9). If the centre of this circle is (alpha, beta), find the value of |alpha - beta|.
- 23
- 14
- 9
- 5
Correct answer: 23
Solution
Using the normal at (6, 9) together with the equal-distance condition to the focus (0, 1) gives the centre (-9, 14), so |alpha - beta| = 23.
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