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If the eccentricity of the hyperbola x² - y² sec² A = 5 equals sqrt(3) times the eccentricity of the ellipse x² sec² A + y² = 25, find a valid value of A.
- pi/4
- pi/6
- pi/3
- pi/2
Correct answer: pi/4
Solution
Setting eₕ² = 3 eₑ² leads to cos² A = 1/2, so cos A = 1/sqrt2 and A = pi/4.
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