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The number of common tangents to the circles $x^{2}+y^{2}=4$ and $x^{2}+y^{2}-6 x-8 y=24$ is
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The centres of the given circles $x^{2}+y^{2}=4$ and $x^{2}+y^{2}-6 x-8 y=24$ are $C_{1}(0,0)$ and $\mathrm{C}_{2}(3,4)$ respectively. Their radii are $\mathrm{r}_{1}=2$ and $r_{2}=7$ respectively.
$\mathrm{C}_{1} \mathrm{C}_{2}=5 < $ sum of radii
But $C_{1} C_{2}=$ difference of radii
Thus, the given circles touch each other internally.
Hence, number of common tangent is only one.
$\mathrm{C}_{1} \mathrm{C}_{2}=5 < $ sum of radii
But $C_{1} C_{2}=$ difference of radii
Thus, the given circles touch each other internally.
Hence, number of common tangent is only one.
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