You are an engineering technician reviewing CAD software specifications for a new hyperbolic cooling tower. The software requires you to input the exact center of the hyperbola to anchor the design grid. Based on the geometric and algebraic properties of hyperbolas, which of the following accurately defines the center of a hyperbola?

An architectural technician is using CAD software to design a hyperbolic cooling tower. To properly anchor the structure on a coordinate grid, the technician must identify the 'center' of the hyperbola using various geometric and algebraic definitions. Match each term below to its correct definition as used in the project specifications.

An architectural technician is using CAD software to model a hyperbolic cooling tower for a power plant. The software requires the technician to identify the primary anchor point of the structure, which is defined as the intersection of the transverse axis and the conjugate axis. In geometric terms, this anchor point is known as the ____ of the hyperbola.

A design technician is using CAD software to model a hyperbolic reflector for a lighting system. The software's technical manual defines the center of the hyperbola as the specific point where the transverse axis and the conjugate axis intersect. Is this definition correct?

Maritime Navigation System Calibration

A CNC machine operator is programming a cutting path along a hyperbolic guide rail. The specification sheet provides the standard equation of the hyperbola as $\frac{(x-5)^2}{16} - \frac{(y+2)^2}{9} = 1$. To set the home position of the cutting tool at the center of this hyperbolic path, the operator must extract the center coordinates (h, k) from the equation.

Arrange the steps below in the correct logical order to determine the coordinates of the center (h, k) from the given equation.

Defining the Center of a Hyperbola in Drafting Software