Respuesta :
Answer:
[tex](x - 3)^{2} + (y - 8)^{2} + (z - 1)^{2} = 30[/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} = 3, y_{c} = 8, z_{c} = 1[/tex]
So
[tex](x - 3)^{2} + (y - 8)^{2} + (z - 1)^{2} = r^{2}[/tex]
through the point (4,3,-1)
This leads us to find the radius.
[tex](4 - 3)^{2} + (3 - 8)^{2} + (-1 - 1)^{2} = r^{2}[/tex]
[tex]r^{2} = 1 + 25 + 4[/tex]
[tex]r^{2} = 30[/tex]
So the equation of the sphere is:
[tex](x - 3)^{2} + (y - 8)^{2} + (z - 1)^{2} = 30[/tex]
