As an entry-level architectural drafter, you are reviewing the design manual for a hyperbolic cooling tower. The manual specifies that the hyperbola used for the cross-section is centered at the origin, with its transverse axis lying strictly on the $x$-axis. To accurately sketch the straight bounding lines that the curves will approach as they extend outward, which of the following pairs of equations must you recall?

As a structural design technician reviewing blueprints for a hyperbolic cooling tower, you must recall the mathematical properties of the boundaries (asymptotes) that guide the shape's curvature. Match each hyperbola characteristic (for a hyperbola centered at the origin) with its correct mathematical equation or geometric description.

A structural design technician is reviewing blueprints for a hyperbolic arch centered at the origin $(0, 0)$. According to the geometric properties of a hyperbola, the asymptotes of the arch correspond to the extended diagonals of its central rectangle. Is this statement True or False?

Asymptote Identification in Hyperbolic Structural Design

Asymptote Equations for Vertical Hyperbolas