Center of a Sphere in R^3(adsbygoogle = window.adsbygoogle || []).push({});

I need to find the center and radius of a sphere given the equation:

[tex]

x^2 - 4x + y^2 + z^2 = 0

[/tex]

I would like to hope it would be as easy as just adding 4x to both sides, but having a variable as the radius probably isn’t correct.

On the other hand, I have no idea how to complete the square when no other coefficients are present. Simply adding y and z coefficients only leads to variables I cannot get rid of on the right side of the equation.

Attempts I have thus far

[tex]

(x-2)^2 + (y+2)^2 + (z+2)^2 = 12 + 4y + 4z

[/tex]

or

[tex]

(x-2)^2+y^2+z^2=(\frac{4}{2})^2

[/tex]

I’m guessing I need to somehow get x^2 on the left and have the sphere centered about the origin.

Any help would be great, thanks.

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# Homework Help: Center of a Sphere in R^3

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