Final answer:
The ordered pairs of the foci of a hyperbola with a horizontal transverse axis and center at the origin are (c, 0) and (-c, 0), where c is the distance from the center to each focus.
Step-by-step explanation:
An elliptical hyperbola with a horizontal transverse axis and center at the origin has its foci on the x-axis. The ordered pairs of the foci are (c, 0) and (-c, 0), where c is the distance from the center to each focus. The value of c can be calculated using the equation c = sqrt(a^2 + b^2), where a is the distance from the center to a vertex and b is the distance from the center to a co-vertex.
For example, if the equation of the hyperbola is x^2/16 - y^2/9 = 1, then a = 4 and b = 3. Substituting these values into the equation c = sqrt(a^2 + b^2), we get c = sqrt(16 + 9) = sqrt(25) = 5. Therefore, the ordered pairs of the foci are (5, 0) and (-5, 0).