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We are tasked with identifying and analyzing the conicoid given by the equation: \[ y^2 + 3z^2 = x \] ### 1. Identify the conicoid The equation \( y^2 + 3z^2 = x \) represents a hyperboloid of one sheet, because: - It's in a form similar to the standard form for a hyperboloid of one sheet, \( \frac{y^2}{a^2} + \frac{z^2}{b^2} = \frac{x}{c^2} \), where the coefficients of \( y^2 \) and \( z^2 ________ __________ _________ __________ _____ _______.
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