Answer:
[tex](x - 5)^{2} + (y - 6)^{2} + (z - 5)^{2} = 62[/tex]
Step-by-step explanation:
The general equation of a sphere is as follows:
[tex](x - x_{c})^{2} + (y - y_{c})^{2} + (z - z_{c})^{2} = r^{2}[/tex]
In which the center is [tex](x_{c}, y_{c}, z_{c})[/tex], and r is the radius.
In this problem, we have that:
[tex]x_{c} = 5, y_{c} = 6, z_{c} = 5[/tex].
So
[tex](x - 5)^{2} + (y - 6)^{2} + (z - 5)^{2} = r^{2}[/tex]
through the point (6, 1, −1)
We use this to find the radius.
[tex](6 - 5)^{2} + (1 - 6)^{2} + (-1 - 5)^{2} = r^{2}[/tex]
[tex]r^{2} = 1 + 25 + 36 = 62[/tex]
So the equation of the sphere is:
[tex](x - 5)^{2} + (y - 6)^{2} + (z - 5)^{2} = 62[/tex]
