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Standard Form of a Horizontal Hyperbola with Center (0, 0)
For a hyperbola centered at the origin, (0, 0), if the -term is positive, its transverse axis lies on the -axis and its branches open left and right. The standard form of this equation is . The hyperbola has vertices and -intercepts at and (a, 0), and it has no -intercepts.
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Intermediate Algebra @ OpenStax
Ch.11 Conics - Intermediate Algebra @ OpenStax
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Related
Focus of a Hyperbola
Transverse Axis of a Hyperbola
Conjugate Axis of a Hyperbola
Standard Form of a Horizontal Hyperbola with Center (0, 0)
Standard Form of a Vertical Hyperbola with Center (0, 0)
Variable Denominators in a Hyperbola Equation
Central Rectangle of a Hyperbola
Asymptotes of a Hyperbola
How to Graph a Hyperbola with Center (0, 0)
Standard Form of the Equation of a Hyperbola with Center (h, k)
Identifying a Hyperbola from its Equation
Branch of a Hyperbola
Center of a Hyperbola
During your onboarding as a junior signal analyst at Global Nav Systems, you are reviewing the mathematical models used to pinpoint locations. The tracking software calculates a target's position based on a curve created by the signal's travel paths to two stationary receiving towers. By definition, which geometric curve is defined as the set of all points in a plane where the difference of their distances from two fixed points is constant?
As a junior technician at an architectural firm, you are reviewing the geometric specifications for a new cooling tower design. The tower's structure is based on a curve where the difference of the distances from any point on the curve to two fixed interior points is constant. To ensure the technical documentation is accurate, match the following geometric terms to their correct definitions.
While working on a CAD (Computer-Aided Design) model for a new telescope lens, a technician observes that the cross-section of a hyperbola is composed of two separate, disconnected curves. Is it true or false that these two distinct parts of the hyperbola are called branches?
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You are an aerospace technician apprentice tracking a deep-space probe. During a planetary gravity assist (slingshot maneuver), the probe's path traces one branch of a hyperbola. To program the trajectory model, you must use the standard geometric definition of a hyperbola. In geometry, a hyperbola is defined as the set of all points in a plane where the ________ of their distances from two fixed points (the foci) is constant.
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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 -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 -intercepts.
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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 . 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 and (a, 0), which means it will have exactly ____ -intercepts.