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.

Drafting a Hyperbolic Cooling Tower

Technical Analysis of a Hyperbolic Signal Reflector