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Let x and y be real numbers satisfying x² + 9y² - 4x + 6y + 4 = 0. Find the maximum value of (4x - 9y).

1. 16
2. 10
3. 22
4. 32

Correct answer: 16

Solution

On the ellipse, 4x - 9y = 11 + 4cos(t) - 3sin(t), whose maximum is 11 + sqrt(16+9) = 16.

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