A technician is mapping a specialized cooling path that follows the hyperbolic trajectory defined by the equation ${}4y^2 - 16x^2 = 64$. After converting the equation to its standard form, rac{y^2}{16} - rac{x^2}{4} = 1, the technician needs to identify the vertices of the graph. According to the standard graphing procedure for this equation, what are the coordinates of the vertices?

An architectural designer is modeling the curvature of a new building facade based on the equation ${}4y^2 - 16x^2 = 64$. To correctly plot this hyperbolic path, arrange the following steps in the standard order of the graphing procedure.

A civil engineer is analyzing the stress lines on a bridge support modeled by the equation ${}4y^2 - 16x^2 = 64$. Match each geometric property of the curve to its corresponding value or description based on the standard form $\frac{y^2}{16} - \frac{x^2}{4} = 1$.

A maintenance technician is mapping a cooling airflow path modeled by the equation ${}4y^2 - 16x^2 = 64$. To begin graphing this curve by converting it into its standard form, $\frac{y^2}{16} - \frac{x^2}{4} = 1$, the technician must divide every term in the equation by the constant value ____.

A network engineer is mapping a signal interference boundary modeled by the equation ${}4y^2 - 16x^2 = 64$. After converting the equation to standard form, the engineer determines that the branches of the hyperbola open upward and downward because the $y^2$-term is positive.