10-1.Circle and System of Circles
medium

वृत्तों $x^2+y^2-18 x-15 y+131=0$ तथा $\mathrm{x}^2+\mathrm{y}^2-6 \mathrm{x}-6 \mathrm{y}-7=0$ के उभयनिष्ठ स्पर्श रेखाओं की संख्या है :

A

$3$

B

$2$

C

$1$

D

$4$

(JEE MAIN-2023)

Solution

$C_1\left(9, \frac{15}{2}\right) \quad r_1=\sqrt{81+\frac{225}{4}-131}=\frac{5}{2}$

$C_2(3,3) r _2=5$

$C_1 C_2=\sqrt{6^2+\frac{81}{4}}=\frac{15}{2}$

$r _1+ r _2=\frac{15}{2}$

$C _1 C _2= r _1+ r _2$

Number of common tangents $=3$

Standard 11
Mathematics

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