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Q.

The length of transverse common tangents to the circles $x^{2} + y^{2} - 2 x - 6 y + 9 = 0$ and $x^{2} + y^{2} + 6 x - 2 y + 1 = 0$ is _______

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answer is 2.

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Detailed Solution

$r_{1} = 1, r_{2} = 3, r_{1} + r_{2} = 4$

$d = \sqrt{20}$

$l e n g t h o f t h e t r a n s v e r s e c o m m o n t a n g e n t = \sqrt{d^{2} - {(r_{1} + r_{2})}^{2}}$

$= \sqrt{20 - {(4)}^{2}}$

$= \sqrt{20 - 16}$

$= \sqrt{4} = 2$

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The length of transverse common tangents to the circles x2+y2−2x−6y+9=0 and x2+y2+6x−2y+1=0 is _______