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Find the eccentricity of the hyperbola that is the locus of the intersection of the lines sqrt(3)x - y - 4*sqrt(3)*t = 0 and sqrt(3)*t*x + t*y - 4*sqrt(3) = 0, where t is a parameter.

1. sqrt(3)
2. 2
3. 2/sqrt(3)
4. 4/3

Correct answer: 2

Solution

Eliminating t produces the hyperbola x²/16 - y²/48 = 1, giving eccentricity sqrt(1 + 48/16) = 2.

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