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# Find the centre and radius of the following spheres :$x^{2}+y^{2}+z^{2}+4x-8x+2z=5$

Toolbox:
• General equation of a sphere $x^2+y^2+z^2+2ux+2vy+2wz+d=0$ centre $(-u, -v, -w)$ radius $= \sqrt{u^2+v^2+w^2-d}$
$x^2+y^2+z^2=4x-8y+2z=5$
The centre is at $( -u, -v, -w)$ where $2u=4, \: 2v=-8, \: 2w=2$ the centre is at $(2, -4, -1)$
The radius = $\sqrt{u^2+v^2+w^2-d}$ with $d=-5$
$\therefore r = \sqrt{4+16+1+5} = \sqrt{26}$ units