Choose the correct statement about two circles whose equations ar… - Vidyadip

MCQ

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
✓
circles have only one meeting point
D
circles have two meeting points

✓

Answer

Correct option: C.

circles have only one meeting point

c
$x^{2}+y^{2}-10 x-10 y+41=0$

$A (5,5), R _{1}=3$

$x^{2}+y^{2}-22 x-10 y+137=0$

$B (11,5), R _{2}=3$

$AB =6= R _{1}+ R _{2}$

Touch each other externally

$\Rightarrow$ circles have only one meeting point.

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