Find an equation of the largest sphere

[Calpalned]

Homework Statement

Find an equation of the largest sphere with center (5, 4, 9) that is contained in the first octant.

Homework Equations

x² + y² + z²

The Attempt at a Solution

[/B]
(x - 5)² + (y - 4)² + (z - 9)² = R²
I am under the impression that R must be no greater than 4, is this true?
My logic stems from the fact that the center is situated at (5, 4, 9), so it is only 4 units away from the y axis. If R > 4, then it will intersect the XZ plane. My textbook does not have answers, so I am not sure if my reasoning is valid.

 

[Borg]

Homework Statement

Find an equation of the largest sphere with center (5, 4, 9) that is contained in the first octant.

Homework Equations

x² + y² + z²

The Attempt at a Solution

[/B]
(x - 5)² + (y - 4)² + (z - 9)² = R²
I am under the impression that R must be no greater than 4, is this true?
My logic stems from the fact that the center is situated at (5, 4, 9), so it is only 4 units away from the y axis. If R > 4, then it will intersect the XZ plane. My textbook does not have answers, so I am not sure if my reasoning is valid.

Yes, that's correct.

 

[HallsofIvy]

Homework Statement

Find an equation of the largest sphere with center (5, 4, 9) that is contained in the first octant.

Homework Equations

x² + y² + z²

The Attempt at a Solution

[/B]
(x - 5)² + (y - 4)² + (z - 9)² = R²
I am under the impression that R must be no greater than 4, is this true?
My logic stems from the fact that the center is situated at (5, 4, 9), so it is only 4 units away from the y axis.

Actually, the crucial point is that it is only 4 units away from the xz- plane.

If R > 4, then it will intersect the XZ plane. My textbook does not have answers, so I am not sure if my reasoning is valid.