Find an equation of the largest sphere

  • Thread starter Calpalned
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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.
 

Answers and Replies

  • #2
Borg
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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.
 
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  • #3
HallsofIvy
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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.
 

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