Circles $x^{2} + y^{2} - 2 x - 4 y = 0 a n d x^{2} + y^{2} - 8 y - 4 = 0$

Touch each other internally

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Touch each other externally

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Cuts each other at two points

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One circle lies inside the other

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Solution

The correct option is A
Touch each other internally

$C_{1} (1, 2), C_{2} (0, 4), R_{1} = \sqrt{5}, R_{2} = 2 \sqrt{5}$

$C_{1} C_{2} = \sqrt{5}$ and $C_{1} C_{2} = | R_{2} - R_{1} |$

Hence circles touch internally.

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