The length of the direct common tangent of the circles $x^{2} + y^{2} - 4 x - 10 y + 28 = 0$ and $x^{2} + y^{2} + 4 x - 6 y + 4 = 0$ is

2

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4

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\sqrt{11}

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16

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Solution

The correct option is A $\sqrt{11}$
From point (12)
length of direct common tangent $= \sqrt{d^{2} - (r_{1} - r_{2})^{2}}$
distance between centres $d = \sqrt{(4)^{2} + (2)^{2}}$
$= \sqrt{20}$
and $r_{1} = 1$ and $r_{2} = 4$
$∴ L = \sqrt{20 - (3)^{2}}$
$L = \sqrt{11}$

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