A CAD technician is modeling a hyperbolic structural support for a new bridge project. To ensure the component is correctly oriented in the design software, the technician must identify the position of the transverse axis. According to the standard form of a hyperbola, which condition ensures that the transverse axis lies horizontally on the $x$-axis?

An apprentice drafter is reviewing the standard form equation for a hyperbolic cooling tower design in a CAD software training module. True or False: If the equation's $x^2$-term is positive, the drafter should recall that the transverse axis of the hyperbola will lie vertically on the $y$-axis.

In technical design and manufacturing, correctly identifying the orientation of hyperbolic components is essential for precision. Match the algebraic condition from a hyperbola's standard form equation with the resulting orientation of its transverse axis.

Orientation Rule for Hyperbolic Structural Components

A CNC programmer is setting up a machine to cut a hyperbolic gear component. The blueprint shows a standard form equation where the $y^2$-term is positive. To properly orient the component, the programmer should recall that the transverse axis lies ____ on the $y$-axis.

Determining Orientation for CAD Hyperboloid Models

An apprentice drafting technician is using CAD software to model a hyperbolic arch for a modern corporate entryway. To correctly align the 3D model in the software workspace, the technician must determine the orientation of the hyperbola's transverse axis from its equation. Arrange the steps the technician should take to identify the correct orientation of the transverse axis, starting from the equation.