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The centre and the radius of the sphere given by $x^{2}+y^{2}+z^{2}-6x+8y-10z+1=0$ is

\[\begin{array}{1 1}(1)(-3 , 4 , -5 ),49 &(2)(-6 , 8 ,-10 ),1 \\(3)(3 , -4 , 5 ),7&(4)(6 , -8 , 10 ),7\end{array}\]

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The equation of the sphere is
$x^2+y^2+z^2-6x+8y-10z+1=0$
Comparing with the equation
$x^2+y^2+z^2+2gx+2fy+2hz+c=0$
Center is $(-g,-f,-h)$
Radius $\sqrt {g^2+f^2+h^2-c}$
Comparing equations
$2g=-6, \; 2f=8\;, 2h=-10,\;c=1$
$g=-3,f=4,h=-5,c=1$
Centre $(3,-4,5)$
Radius $\sqrt {(-3)^2+4^2+(-5)^2-1}$
$\qquad= \sqrt {9+16+25-1}$
$\qquad= \sqrt {49}=7$
Hence 3 is the correct answer.
answered May 13, 2014 by meena.p
 

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