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The hyperbola defined by |sqrt((x-1)² + (y-2)²) - sqrt((x-5)² + (y-5)²)| = 3 has a conjugate hyperbola with eccentricity e'. Find 4*e'.

1. 4
2. 5
3. 8
4. 10

Correct answer: 10

Solution

For the conjugate hyperbola, a and b swap roles: its a' = b = 2 and b' = a = 3/2. Eccentricity of conjugate: e' = sqrt(1 + (b')²/(a')²) = sqrt(1 + (9/4)/4) = sqrt(1 + 9/16) = sqrt(25/16) = 5/4. So 4*e' = 5.

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