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Complete the square to write the equation of the sphere in standard form.?

0 votes

x^2 + y^2 + z^2 + 7x - 2y + 12z + 22 = 0

asked Jul 5, 2014 in PRECALCULUS by anonymous

1 Answer

–1 vote

The sphre equation is image

Standard form of a sphere equation is image

Where (h, ,j , k ) is center and r is radius of sphere.

image

Separate variables and constants aside by subtracting 22  from each side.

image

To complete the squre add (half cooefficient of x ) 2, (half cooefficient of y ) 2 and (half cooefficient of z ) 2to each side of the expression.

x  coefficient = 7 then (half the x coefficient)² is (7/2) 2 = 49/4.

y coefficient = - 2 then (half the y coefficient)² is (-2/2) 2 = 1.

z  coefficient = 12 then (half the z coefficient)² is (12/2) 2 = 36.

image

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image

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Compare it to image

image.

 

answered Jul 5, 2014 by david Expert

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