Hyperbolic Design Framework

In technical drafting and architectural layout, the central rectangle of a hyperbola is a critical construction guide. Match each component of the rectangle with its specific role in the graphing process.

In technical drafting and design, a 'central rectangle' is often constructed to assist in graphing a hyperbola centered at {}0, 0. Is it true or false that the sides of this rectangle are designed to intersect the coordinate axes at the hyperbola's vertices $(\pm a, 0)$ and the points $(0, \pm b)$?

You are updating a technical drafting manual for an engineering firm that designs hyperbolic cooling towers. Complete the following guideline for the new design trainees:

"To accurately sketch the boundaries of the curve, first construct the central rectangle using the vertices and the conjugate axis endpoints. The extended diagonals of this central rectangle form the ________ of the hyperbola, which guide the precise shape of the outward curves."

Drafting Guidelines for a Hyperbolic Structure

As a junior CAD (Computer-Aided Design) layout technician, you are drafting a template for a hyperbolic reflector. To correctly position the guide lines (asymptotes) in your software, you need to follow the standard geometric construction sequence for the central rectangle of a hyperbola centered at {}(0, 0) with a horizontal transverse axis.

Arrange the following drafting steps in the correct chronological order to construct the central rectangle and define the hyperbola's asymptotes.