The locus of intersection of two lines \sqrt3 x - y = 4k\sqrt3 and k(\sqrt3 x + y) = 4\sqrt3 for different values of k is a hyperbola. The eccentricity of the hyperbola'is

NIMCET 2014 Question Paper with solutions

Question : 4 of 120

Marks: +1, -0

The locus of intersection of two lines

√3 x

- y = 4k

√3

and

k(√3 x + y)

4√3

for different values of k is a hyperbola. The eccentricity of the hyperbola'is

Solution:

Given, lines are

√3x

- y = 4 k

√3

... (i)
k

(√3x)

+ ky = 4

√3

⇒

√3x

+ y =

{4√3}/k

... (ii)
From eqs (i) and (ii)

3x^2-y^2

= 48

x^2/{16}

y^2/{48}

= 1
which is a hyperbola
∴ a = 4 , b =

4√3

e =

√{1+b^2/a^2}

√{{16+48}/{16}}

√{{64}/{16}}

= 2

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