C₁ and C₂ are circles of unit radius with centers at (0, 0) amd (1, 0) respectively C₃ is a circle of unit radius passes through the centers of circles C1and C₂ are have its center above X-axis. The equation of common tangent to C₁ and C₃which does into pass through C₂ is

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$x - \sqrt{3} y + 2 = 0$

$\sqrt{3} x - y + 2 = 0$

$\sqrt{3} x - y - 2 = 0$

$x + \sqrt{3} y + 2 = 0$

answer is B.

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Detailed Solution

Equation of circle through (0, 0) and (1, 0) is
$x^{2} + y^{2} - x + λy = 0$
It represents C₃ its radius is 1. $\Rightarrow λ = - \sqrt{3}$
their common tangents are parallel to line joining their centres (0, 0) and $(\frac{1}{2}, \frac{\sqrt{3}}{2})$
equation of common tangent is $\sqrt{3} x - y + k = 0$
$\Rightarrow r = d \Rightarrow k = \pm 2$
Hence its equation is $\sqrt{3} x - y + 2 = 0$