Respuesta :
Answer:
[tex](x - 5)^{2} + (y - 4)^{2} + (z - 9)^{2} = 16[/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} = 4, z_{c} = 1[/tex]
So
[tex](x - 5)^{2} + (y - 4)^{2} + (z - 9)^{2} = r^{2}[/tex]
Interior contained in the first octant:
The first octant is bounded by:
The xy plane, in which z is 0. The distance from the center of the sphere to the xy plane is 9.
The xz plane, in which y is 0. The distance from the center of the sphere to the xz plane is 4.
The yz plane, in which x is 0. The distance from the center of the sphere to the yz plane is 5.
This means that if the radius is higher than four, the sphere will cross into a different octant.
So the radius for the largest sphere is 4.
The equation is
[tex](x - 5)^{2} + (y - 4)^{2} + (z - 9)^{2} = 4^{2}[/tex]
[tex](x - 5)^{2} + (y - 4)^{2} + (z - 9)^{2} = 16[/tex]
