Two circles {x^2} + {y^2} - 2x + 6y + 6 = 0 and {x^2} + {y^2} - 5x + 6y + 15 = 0 touch each other. e

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10-1.Circle and System of Circles

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The two circles ${x^2} + {y^2} - 2x + 6y + 6 = 0$ and ${x^2} + {y^2} - 5x + 6y + 15 = 0$ touch each other. The equation of their common tangent is

A

$x = 3$

B

$y = 6$

C

$7x - 12y - 21 = 0$

D

$7x + 12y + 21 = 0$

Solution

(a) Let $S_1 \equiv x^2 + y^2 -2x + 6y + 6 = 0$

and $S_2 \equiv x^2 + y^2 -5x + 6y + 15 = 0,$

then common tangent is $S_1 -S_2 = 0$

$==> 3x = 9 $

$==> x = 3 .$

Standard 11

Mathematics

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