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

Question

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

Answer 1

The sphre equation is

Standard form of a sphere equation is

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

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

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.

Compare it to

.