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A hyperbola x²/a² - y²/b² = 1 (a, b > 0) passes through the intersection 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 b.
- 4
- 2*sqrt(2)
- 4*sqrt(2)
- 8/5
Correct answer: 4
Solution
The lines meet at (5, 4); substituting and using 2b²/a = 32sqrt(2)/5 yields b = 4.
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