Word Count : 469

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To show that the plane \( 2x + y + 2z = 0 \) is tangent to the sphere \( x^2 + y^2 + z^2 - 2x + 2y - 2z + 2 = 0 \), we need to follow these steps: ### Step 1: Find the center and radius of the sphere The given equation of the sphere is: \[ x^2 + y^2 + z^2 - 2x + 2y - 2z + 2 = 0 \] We can rewrite this equation by completing the square for each variable: - For \( x^2 ________ _________ __________ _________ ___.
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