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10-1.Circle and System of Circles
medium
Choose the correct statement about two circles whose equations are given below
$x^{2}+y^{2}-10 x-10 y+41=0$
$x^{2}+y^{2}-22 x-10 y+137=0$
A
circles have same centre
B
circles have no meeting point
C
circles have only one meeting point
D
circles have two meeting points
(JEE MAIN-2021)
Solution
$x^{2}+y^{2}-10 x-10 y+41=0$
$A (5,5), R _{1}=3$
$x^{2}+y^{2}-22 x-10 y+137=0$
$B (11,5), R _{2}=3$
$AB =6= R _{1}+ R _{2}$
Touch each other externally
$\Rightarrow$ circles have only one meeting point.
Standard 11
Mathematics
