person123466 person123466

16-01-2021
Mathematics

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show that x^2 + y^2 + z^2 = 3(2x-y) -1 is a sphere

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ChoiSungHyun ChoiSungHyun

16-01-2021

Step-by-step explanation:

x² + y² + z² = 3(2x - y) - 1

x² + y² + z² = 6x - 3y - 1

x² - 6x + y² + 3y + z² = -1

(x - 3)² + (y + 1.5)² + z² = -12.25

(x - 3)² + (y + 1.5)² + z² = -(3.5)²

Since it follows the general equation form, it is a sphere.

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