If the circle x^2+y^2-6x-12y+1=0 cuts another | vedclass

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(A) The given circle is $x^2+y^2-6x-12y+1=0$. Comparing this with $x^2+y^2+2g_1x+2f_1y+c_1=0$,we get $g_1=-3, f_1=-6, c_1=1$.Let the circle $C$ be $x^

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$\sqrt{21}$

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(A) The given circle is $x^2+y^2-6x-12y+1=0$. Comparing this with $x^2+y^2+2g_1x+2f_1y+c_1=0$,we get $g_1=-3, f_1=-6, c_1=1$.Let the circle $C$ be $x^2+y^2+2g_2x+2f_2y+c_2=0$. Given the centre is $(-4, 2)$,so $-g_2=-4 \Rightarrow g_2=4$ and $-f_2=2 \Rightarrow f_2=-2$.Two circles cut orthogonally if $2g_1g_2+2f_1f_2=c_1+c_2$.Substituting the values: $2(-3)(4) + 2(-6)(-2) = 1 + c_2$.$-24 + 24 = 1 + c_2 \Rightarrow c_2 = -1$.The radius $r$ of circle $C$ is given by $\sqrt{g_2^2+f_2^2-c_2}$.$r = \sqrt{4^2+(-2)^2-(-1)} = \sqrt{16+4+1} = \sqrt{21}$.

If the circle $x^2+y^2-6x-12y+1=0$ cuts another circle $C$ orthogonally and the centre of the circle $C$ is $(-4, 2)$,then its radius is

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