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If the line 3x + 4y = 12*sqrt(2) is tangent to the ellipse x²/a² + y²/9 = 1 for some real a, find the distance between the foci of this ellipse.

1. 2*sqrt(7)
2. 4
3. 2*sqrt(5)
4. 2*sqrt(2)

Correct answer: 2*sqrt(7)

Solution

From the tangency condition c² = a² m² + b² we solve for a² = 16, then b² = 9 gives c = ae with a² e² = a² - b² = 7, so distance between foci 2ae = 2 sqrt7.

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