Find an equation of the largest sphere

  • Thread starter Calpalned
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  • #1
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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
Science Advisor
Gold Member
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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.
 
  • #3
HallsofIvy
Science Advisor
Homework Helper
41,847
969

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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