Final answer:
The equation of the sphere in standard form is (x - h)² + (y - k)² + (z - l)² = r² where (h, k, l) is the center of the sphere and r is the radius. To write the given equation in standard form, we need to complete the square.
Step-by-step explanation:
The equation of the sphere in standard form is:
(x - h)² + (y - k)² + (z - l)² = r²
where (h, k, l) is the center of the sphere and r is the radius.
To write the given equation in standard form, we need to complete the square.
First, group the x, y, and z terms together on one side of the equation.
Then, move the constant term to the other side.
Next, divide all the terms by the coefficient of the squared terms to make it 1.
Finally, rewrite the equation in standard form by completing the square.
Applying these steps to the given equation, we get:
(x - 2)² + (y + 1)² + (z - 0)² = 9