The locus of the point of intersection of the lines `sqrt(3)x-y-4sqrt(3)lambda=0\ a n d\ sqrt(3)lambdax+lambday-4sqrt(3)=0` is a hyperbola of eccentricity
a.`1`
b. `2`
c. `3`
d. `4`

Explanation

`sqrt{3} x-y-4 sqrt{3} lambda=0` and `sqrt{3} lambda+lambda-4 sqrt{3}=0` can be rewritten as `sqrt{3} x-y=4 sqrt{3} lambda` and `sqrt{3} lambda+lambda=4 sqrt{3}`

Multiplying the equations

`3 lambda x^{2}-lambda y^{2}=48 lambda `

`Rightarrow frac{3 lambda x^{2}}{48 lambda}-frac{lambda y^{2}}{48 lambda}=1 `

`Rightarrow frac{x^{2}}{16}-frac{y^{2}}{48}=1`

standard equation of a hyperbola `a^{2}=16` and `b^{2}=48`.

`e=sqrt{frac{a^{2}+b^{2}}{a^{2}}}`

`Rightarrow e=sqrt{frac{16+48}{16}} `

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