Question

How do you find an equation of the sphere with center (4,3,5) and radius √6?

Answer 1

`(x-4)^2+(y-3)^2+(x-5)^2=6`

Explanation:

The the center of the sphere is given as (a,b,c) and the radius is r, then the equation of the sphere would be:

`(x-a)^2+(y-b)^2+(x-c)^2=r^2`

From the info, we can say:

a = 4

b = 3

c = 5

r =
`√(6)`

Plugging into formula we get the equation:

`(x-a)^2+(y-b)^2+(x-c)^2=r^2\\(x-4)^2+(y-3)^2+(x-5)^2=(√(6) )^(2) \\(x-4)^2+(y-3)^2+(x-5)^2=6`

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