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Number of Common Tangents to Two Circles in Different Conditions

The two circl...

Question

The two circles $x^{2} + y^{2} - 4 y = 0$ and $x^{2} + y^{2} - 8 y = 0$

A

Touch each other internally

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B

Touch each other externally

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C

Do not touch each other

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D

intersect each other

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Solution

The correct option is A
Touch each other internally

$r_{1} = 2; r_{2} = 4$

$C_{1} C_{2} = 2$

∵ $r_{2} - r_{1} = C_{1} C_{2}$

$∴$ Circle touches internally.

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x^{2} + y^{2} - 2 x - 4 y = 0

x^{2} + y^{2} - 8 y - 4 = 0

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