The locus of the point of intersection of the lines 3 k x + k y - 4 3 = 0 and 3 x - y - 4 3 k = 0 is a conic, whose eccentricity is

Question

The locus of the point of intersection of the lines 3 k x + k y - 4 3 = 0 and 3 x - y - 4 3 k = 0 is a conic, whose eccentricity is,

MARKS App · Accepted Answer

The point of intersection of the lines 3 k x + k y - 4 3 = 0 and 3 x - y - 4 3 k = 0 . k = 4 3 3 x + y = 3 x - y 4 3 ⇒ 3 x 2 - y 2 = 48 ⇒ x 2 16 - y 2 48 = 1 Which is a hyperbola. b 2 = a 2 e 2 - 1 Now, 48 = 16 e 2 - 1 ⇒ e = 4 = 2

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