Question

Write the given equation in the form of an equation of a sphere and find its center and radius.

x2 + y2 + z2 = 12x + 2y
equation =

center (x, y, z) =

radius =

Answer 1

Answer:The radius is the square root of the constant term, z

Explanation:

edge 2021

Answer 2

Complete whatever squares you can:

x² - 12x = x² - 12x + 36 - 36 = (x - 6)² - 36

y² - 2y = y² - 2y + 1 - 1 = (y - 1)² - 1

So rewrite the equation as

x² + y² + z² = 12x + 2y

→ x² - 12x + y² - 2y + z² = 0

→ (x - 6)² - 36 + (y - 1)² - 1 + z² = 0

→ (x - 6)² + (y - 1)² + z² = 37

Then the center is (x, y, z) = (6, 1, 0), and its radius is √(37).