An engineer is using the standard form equation of a hyperbola to model the curvature of a cooling tower. To correctly analyze the model, which rule must they use to identify the denominator $a^2$?

An architectural technician is analyzing the standard form equation for a hyperbolic arch to determine its structural orientation. To identify the transverse axis, they must first locate $a^2$. In the standard form equation of a hyperbola, $a^2$ is defined as the denominator of the ________ term, regardless of whether it is larger or smaller than the other denominator.

A landscape architect is designing a hyperbolic fountain for a city park. They are using the equation $\frac{y^2}{16} - \frac{x^2}{25} = 1$ to determine the curvature of the structure. True or False: In this standard form equation, $a^2$ is equal to 25 because it is the larger of the two denominators.

An architectural technician is designing a modern building with a hyperbolic roof. To correctly interpret the structural equations for the blueprint, the technician must recall the specific rules for identifying variables in the standard form. Match each component of the hyperbola's standard equation with the rule used to identify it.

Identifying Hyperbolic Parameters for Precision Machining

A junior CNC machining technician is setting up a precision lathe to manufacture a hyperbolic reflector shield. The product blueprint provides the hyperbola's standard form equation. To correctly program the tool path, the technician must locate the parameter $a^2$ and determine the orientation of the transverse axis. Arrange the steps below in the correct logical sequence the technician must follow.