The locus of the point of intersection of lines √3x - y - 4√3k = 0 and √3 kx + ky - 4√3 = 0 for different value of k

Question

State whether the statements True or False. Justify

The locus of the point of intersection of lines √3x - y - 4√3k = 0  and √3 kx + ky - 4√3 = 0 for different value of k is a hyperbola whose eccentricity is 2.

Answer 1

Equating the values of k,

48 = 16 (e² - 1)

e² - 1 = 3

e² = 4

e = 2

Hence, the eccentricity of the given hyperbola is 2, which makes the statement correct, and it is TRUE.