Word Count : 554

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### Let's analyze each of the given conicoids one by one. #### (i) \( x^2 + y^2 + x^2 + 4x + 3y - z = 0 \) 1. Simplify the equation: \[ 2x^2 + y^2 + 4x + 3y - z = 0 \] This represents a second-order surface, and we will check if it is central or non-central. 2. Identifying if it is central: A conicoid is central if the equation has no linear terms (i.e., the terms involving \( x \), \( y \), and \( z \) are not present). Here, we have linear terms in \( x \) and \( y \) (\( 4x + 3y \)), so this conicoid is non-central. 3. Finding the center: To determine the center, we need to complete the square for the \( x \)-terms and \( ________ _____ _______ ____ _______ ___ ______.
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