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  4. The locus of the center of a variable circle which always touches two given circles externally is

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Q. The locus of the center of a variable circle which always touches two given circles externally is

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Solution:

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$O O_{1}=r+r_{1}$
$O O_{2}=r+r_{2}$
$\therefore O O_{2}-O O_{1}=r_{2}-r_{1}$
hence, locus is hyperbola