Circles {x^2} + {y^2} = 9 and {x^2} + {y^2} - 12y + 27 = 0 touch each other. equation of their commo

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10-1.Circle and System of Circles

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The circles ${x^2} + {y^2} = 9$ and ${x^2} + {y^2} - 12y + 27 = 0$ touch each other. The equation of their common tangent is

A

$4y = 9$

B

$y = 3$

C

$y = - 3$

D

$x = 3$

Solution

(b) ${S_1} = {x^2} + {y^2} – 12y + 27 = 0$

${S_2} = {x^2} + {y^2} – 9 = 0$

The equation of common tangent is

${S_1} – {S_2} = 0 $

$\Rightarrow – 12y + 36 = 0$

$\Rightarrow y = 3$.

Standard 11

Mathematics

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