Answer:
- x² +(y +5)² +(z +3)² = 49
- center: (0, -5, -3)
- radius: 7
Explanation:
You want the equation of the sphere in standard form, and its center and radius.
x² +y² +z² +10y +6z = 15
Solution
Completing the squares for the y and z terms we have ...
x² +(y² +10y +25) +(z² +6z +9) = 15 +25 +9
x² +(y +5)² +(z +3)² = 49
Comparing this to the standard form equation for a sphere centered at (a, b, c) with radius r, we can find the center and radius.
(x -a)² +(y -b)² +(z -c)² = r²
a = 0, b = -5, c = -3, r = 7
The sphere is centered at (x, y, z) = (0, -5, -3) and has radius 7.
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