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The question reads x^2+y^2-14y+z^2 >= -13. Describe the solid the equation describes.

After completing the square and all that I get an equation of the sphere where:

x^2+(y-7)^2 +z^2 is greater than or equal to -13. Thus the equation describes a sphere centered at (0,7,0) with an undefined radius?. However by the back of the book the radius is actually 6. Where am I going wrong??

Thank you

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    `greater than or equal to -13` Recheck your calculations, you lost a constant term along the way. Also note that the inequality will not give a sphere, but rather the interior or exterior of a sphere. – 2017-01-23

1 Answers 1

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The equation is $x^2+(y-7)^2 +z^2\ge 36=6^2$ (you need to add $49$ on both sides in order to complete the square), so the solid is the exterior (complement) of the open ball centered in $(0,7,0)$ with radius $6$