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Find the eccentricity of the conic that is the locus of the intersection of the lines sqrt(3)*k*x + k*y - 4*sqrt(3) = 0 and sqrt(3)*x - y - 4*sqrt(3)*k = 0, as k varies.

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

Correct answer: 2

Solution

Eliminating k gives 3x² - y² = 48, a hyperbola of the form x²/16 - y²/48 = 1 with e = 2.

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