If one of diameters of circle x^{2}+y^{2}-2 x-6 y+6=0 is a chord of another circle 'C' , who

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10-1.Circle and System of Circles

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If one of the diameters of the circle $x^{2}+y^{2}-2 x-6 y+6=0$ is a chord of another circle $'C'$, whose center is at $(2,1),$ then its radius is..........

A

$2$

B

$3$

C

$6$

D

$4$

(JEE MAIN-2021)

Solution

$x^{2}+y^{2}+2 x-6 y+6=0$

center $(1,3)$

radius $=2$

distance between $(1,3)$ and $(2,1)$ is $\sqrt{5}$

$\therefore(\sqrt{5})^{2}+(2)^{2}=r^{2}$

$\Rightarrow r =3$

Standard 11

Mathematics

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(JEE MAIN-2019)