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To determine which of the given conicoids are central and which are non-central, and to identify if the central conicoids have their center at the origin, we will analyze the equations using the general form of a conicoid and apply the properties related to their center. ### (i) \( x^2 + y^2 + z^2 + 4x + 3y - z = 0 \) Step 1: Completing the square for each variable - For \( x^2 + 4x \), complete the square: \( x^2 + 4x = (x + 2)^2 - 4 \) - For \( y^2 + 3y \), complete the square: \( y^2 + 3y = (y + \frac{3}{2})^2 - \frac{9}{4} \) - For \( z^2 ___ _______ _________ ____ _________ __________ _______.
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