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The locus of the center of a variable circle which always touches two given circles externally is
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The correct answer is:
a hyperbola
$\begin{array}{l}
\mathrm{oo}_{1}=\mathrm{r}+\mathrm{r}_{1} \\
\mathrm{oo}_{2}=\mathrm{r}+\mathrm{r}_{2} \\
\therefore \mathrm{oo}_{2}-\mathrm{oo}_{1}=\mathrm{r}_{2}-\mathrm{r}_{1}
\end{array}$
hence, locus is hyperbola
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