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The line x - 2y = 12 touches the ellipse x²/a² + y²/b² = 1 at the point (3, -9/2). Find the length of the latus rectum of this ellipse.
- 9
- 8sqrt(3)
- 12sqrt(2)
- 5
Correct answer: 9
Solution
Matching the tangent at (3, -9/2) to x - 2y = 12 gives a² = 36, b² = 27; latus rectum = 2b²/a = 2*27/6 = 9.
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