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If the latus rectum of a hyperbola subtends a right angle at the other focus, find the eccentricity of the hyperbola.
- cot(pi/8)
- tan(pi/8)
- 1 - sqrt(2)
- 1/(sqrt(2) - 1)
Correct answer: cot(pi/8)
Solution
Setting (b²/a)/(2ae) = tan45 = 1 gives e² - 2e - 1 = 0, so e = 1 + sqrt(2) = cot(pi/8).
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