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mintygreen
05-02-2010, 07:35 PM
Hi there,

I'm really not sure what to do with this problem:

Find an equation of the largest sphere that passes through the points (-1,1,4) and is such that each of the points (x,y,z) inside the sphere satisifies the condition

x^2+y^2+z^2 < 136+ 2(x+2y+3z)

I assume I take x^2 + y^2 + z^2 as f(x,y,z) and 2x + 4y + 6z = -136 as g(x,y,z)=k ? But I'm not sure how to deal with the inequality or how to set it so the sphere passes through the point. I'd really appreciate some help!

Thanks,
Ella