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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