10-1.Circle and System of Circles
hard

वृत्तों $x^{2}+y^{2}-4 x-6 y-12=0$ तथा $x^{2}+y^{2}+6 x+18 y+26=0$ की उभयनिष्ठ स्पर्श रेखाओं की संख्या है

A

$4$

B

$1$

C

$2$

D

$3$

(JEE MAIN-2015)

Solution

$c_{1}(2,3);$

$r_{1}=\sqrt{4+9+12}=5$

And $c_{2}(-3,-9)$

$r_{2}=\sqrt{9+81-26}=8$

$\therefore \quad$ Distance $c_{1} c_{2}=\sqrt{25+144}=13$

$\therefore \quad c_{1} c_{2}=r_{1}+r_{2}$ touching externally.

$\Rightarrow \quad 3$ common tangents.

Standard 11
Mathematics

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