The locus of the centre of a variable circle touching \( \mathrm{P}...

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The locus of the centre of a variable circle touching
\( \mathrm{P} \) two circles of radius \( r_{1} \) and \( r_{2} \) externally, which also

W touch each other externally, is a conic. The eccentricity of the conic, if \( \frac{r_{1}}{r_{2}}=3+2 \sqrt{2} \), is
(1) 1
(2) \( \sqrt{2} \)
(3) \( \frac{1}{2} \)
(4) \( 2 \sqrt{2} \)
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