About x^2 + y^2 +z^2 = 2z?
I understand that the equation (x^2 + y^2 + z^2 = 2z) represents a sphere, and I believe it involves a shift. However, I'm having difficulty grasping how to graph this equation without a calculator. Can anyone explain why the sphere is shifted, or suggest an alternative way to represent this equation that might help clarify its behavior?
3 Answers
x² + y² + z² = 2z
x² + y² + z² - 2z = 0
x² + y² + z² - 2z + 1 = 1
x² + y² + (z - 1)² = 1
Center (0,0,1)
Radius = 1
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