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For the given equation of a sphere, write the equation in standard form. Then find the center and radius. 8) [8] x2 + y2 + z2 + 10y + 6z = 15

Respuesta :

sqdancefan

Answer:

  • x² +(y +5)² +(z +3)² = 49
  • center: (0, -5, -3)
  • radius: 7

Step-by-step 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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