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posted by  Need Chem help on 8/29/2009 6:05:50 PM  |  status: Closed  |  Earned Karma: 36

Calc 3 help please!!!

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N/A N/A N/A N/A 8/2/2009 at 6:00:00 AM
Question Details:

Find an equation of the sphere that passes through the origin and whose center is (10, 9, -9).

__________________________________________ = 0
Note that you must put everything on the left hand side of the equation and that we desire the coefficients of the quadratic terms to be 1.


Find an equation of the largest sphere with center (9, 2 , 4) that is contained completely in the first octant.

= 0
Note that you must move everything to the left hand side of the equation that we desire the coefficients of the quadratic terms to be 1.

Tags: Calculus
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posted by Grace on 8/29/2009 6:16:56 PM  |  status: Live
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Response Details:
Equations for spheres take the general form:
(x - a)2 + (y - b)2 + (z - c)2 = r2
where the center is (a, b, c) and r is the radius.

1. So the equation of the sphere given center (10, 9, -9) is (x - 10)2 + (y - 9)2 + (z + 9)2 .
Now you have to make sure that it passes through the origin so you want to plug in (0, 0, 0).
(0 - 10)2 + (0 - 9)2 + (0 + 9)2 = 262, which is r2.
So the equation is: (x - 10)2 + (y - 9)2 + (z + 9)2 - 262 = 0

2. (x - 9)2 + (y - 2)2 + (z - 4)2 = r2
Look at each of the coordinates to find which will give you radius completely contained in the first octant. The coordinate values must all be positive to be in the first octant.
You can't move 9 units on either side of the y and z coordinates or you would get negative values.
2 units can work since it wouldn't make x or z negative.
4 units would make y negative.

Therefore r = 2 and r2 = 4 and your equation is: (x - 9)2 + (y - 2)2 + (z - 4)2 - 4 = 0
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