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# Find the center and radius of the sphere x^{2} + y^{2} + z^{2} - 6y + 8z = 0.

**Solution:**

We have equation of the sphere centred at (h, k. l) and having radius r is given by

(x - h)^{2 }+ (y - k)^{2 }+ (z - l)^{2 }= r^{2}---------------------------(1)

To identify the centre and radius of the given sphere we have to convert the given equation

x^{2} + y^{2} + z^{2} - 6y + 8z = 0 to the form in equation (1)

Now group the x , y and z terms and by completing the square, we get

x^{2 }+ (y^{2 }- 6y + 9) +(z^{2 }+ 8z + 16) = 9 + 16

(x - 0)^{2} + (y - 3)^{2 }+ (z + 4)^{2 }= 5^{2}

Hence centre of the sphere is (0, 3, -4) and radius = 5

## Find the center and radius of the sphere x^{2} + y^{2} + z^{2} - 6y + 8z = 0.

**Summary: **

The center and the radius of the sphere with the equation, x^{2} + y^{2} + z^{2} - 6y + 8z = 0 are (0, 3, -4) and 5 respectively.

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