Given the equation of a sphere
Which of the following is the vector equation of the sphere above?
Given the equation of the sphere
x^2+y^2+z^2-yx+2y+2z=-5\\\implies xx^2-4x+y^2+2y+z^2+2z=-5\\\implies (x^2-4x+2^2-2^2)+(y^2+2y+1-1)+(z^2+2Z+1-1)=-5\\ [(x-2)^2-4]+[(y+1)^2-1]+[(z+1)^2-1]=-5\\\implies (x-2)^2+(y+1)^2+(z+1)^2-6=-5\\\implies (x-2)^2+(y+1)^2+(z+1)^2=1\\
centre of sphere
radius of sphere
vector form is
Hence option 2 is correct
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