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A hyperbola x²/a² - y²/b² = 1 passes through the intersection point of the lines 7x + 13y - 87 = 0 and 5x - 8y + 7 = 0, and its latus rectum is 32*sqrt(2)/5. Find the value of 2a² + b².
- 41
- 26
- 30
- 34
Correct answer: 41
Solution
The lines meet at (5, 4); using the latus rectum 32 sqrt2/5 gives a² = 25/2 and b² = 16, so 2a² + b² = 25 + 16 = 41.
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