A manufacturing technician is reviewing the geometric specifications for a new line of curved structural components. Match each characteristic of a horizontal hyperbola centered at the origin (0, 0) with its correct mathematical property or description as defined in the technical manual.

An architectural drafter is programming a CNC machine to cut a custom structural support. The design manual specifies that the cut must follow a horizontal hyperbola centered at the origin, (0, 0), with the branches opening left and right along the $x$-axis. To accurately model this shape in the drafting software, which standard form equation should the drafter recall and enter?

A manufacturing technician is evaluating a part design modeled by the equation rac{x^2}{a^2} - rac{y^2}{b^2} = 1, centered at the origin (0, 0). True or False: According to this mathematical model, the curved edge of the part will have no $y$-intercepts.

Identifying Mounting Vertices for a Hyperbolic Structural Brace

Identifying Mounting Points for a Hyperbolic Reflector

A design technician is programming a CNC router to cut a decorative groove along a path modeled by a horizontal hyperbola centered at the origin, (0, 0). The blueprint defines this path using the standard equation $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$. When defining the outer clearance boundary, the technician recalls that because the branches of this horizontal hyperbola only open left and right, the path will have vertices at $(-a, 0)$ and (a, 0), which means it will have exactly ____ $y$-intercepts.