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Example: Graphing
To graph the equation , first convert it to standard form by dividing every term by 64: , which simplifies to . Since the -term is positive, the transverse axis is vertical. From , we get , so the vertices are and . From , we get . Sketch the central rectangle intersecting the -axis at and and the -axis at the vertices. Sketch the asymptotes through the diagonals of the rectangle. Finally, draw the two branches of the hyperbola through the vertices, opening upward and downward.
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Ch.11 Conics - Intermediate Algebra @ OpenStax
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Example: Graphing
Example: Graphing
How to Graph a Hyperbola with Center
As a junior designer at an engineering firm, you need to create a preliminary manual sketch of a hyperbolic cooling tower profile centered at the origin, . To accurately set up the geometric framework for the blueprint, arrange the standard steps for graphing a hyperbola in the correct chronological order.
An engineering technician is drafting a blueprint for a hyperbolic cooling tower centered at the origin, . According to the standard graphing procedure, which characteristic of the equation in standard form is used to determine whether the transverse axis is horizontal or vertical?
As a junior technician at an urban planning firm, you are assisting in the layout of a park with hyperbolic-shaped walkways centered at . To ensure the layout is geometrically sound, match each geometric component of the 6-step graphing procedure with its specific role in defining the hyperbola's layout.
Defining the Geometric Framework for Hyperbolic Design
In the technical drafting of a hyperbolic cooling tower profile centered at the origin, , the standard graphing procedure specifies that the asymptotes are constructed by drawing lines through the diagonals of the central rectangle.
Learn After
A technician is mapping a specialized cooling path that follows the hyperbolic trajectory defined by the equation . After converting the equation to its standard form, rac{y^2}{16} - rac{x^2}{4} = 1, the technician needs to identify the vertices of the graph. According to the standard graphing procedure for this equation, what are the coordinates of the vertices?
An architectural designer is modeling the curvature of a new building facade based on the equation . To correctly plot this hyperbolic path, arrange the following steps in the standard order of the graphing procedure.
A civil engineer is analyzing the stress lines on a bridge support modeled by the equation . Match each geometric property of the curve to its corresponding value or description based on the standard form .
A maintenance technician is mapping a cooling airflow path modeled by the equation . To begin graphing this curve by converting it into its standard form, , the technician must divide every term in the equation by the constant value ____.
A network engineer is mapping a signal interference boundary modeled by the equation . After converting the equation to standard form, the engineer determines that the branches of the hyperbola open upward and downward because the -term is positive.