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Find an equation of the sphere that passes through the point $ (4, 3, -1) $ and has center $ (3, 8, 1) $.

$(x-3)^{2}+(y-8)^{2}+(z-1)^{2}=30$

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Johns Hopkins University

Oregon State University

Harvey Mudd College

University of Nottingham

So you don't find the equation of sphere that passes through this point and has this center. So we know that we can write the equation of a sphere with each center co ordinate, like so need to find our squared. We don't know our square. So we're going to take this point here and plug it in here. So we got four minus three squared, plus three minus eight squared plus negative one minus one squared is equal to R squared. We got one squared plus negative five squared, plus native to squared is equal to R squared. So that one plus twenty five plus four is equal to R squared and Nazi. Pull that thirty. Okay, Our square is equal to thirty. So then we can rewrite our equation like this.