# 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.

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.

## Homework Statement

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

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.

• Calpalned

## Homework Statement

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

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.