ALGEBRA II HYPERBOLAS A HYPERBOLA CAN HAVE A

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Algebra II - Hyperbolas


A hyperbola can have a vertical or horizontal transverse axis. A hyperbola that is centered at the origin with a horizontal transverse axis has an equation of the form ALGEBRA II HYPERBOLAS A HYPERBOLA CAN HAVE A . A hyperbola that is centered at the origin with a vertical transverse axis has an equation of the form ALGEBRA II HYPERBOLAS A HYPERBOLA CAN HAVE A . When graphing a hyperbola you must be able to find the vertices, the slopes of the asymptotes, and the foci. Refer to your notes for this if necessary.


Notes on hyperbolas:


In the standard equations above, a is the distance from the center of the hyperbola to each vertex, so if the transverse axis is horizontal, the vertices are located at ALGEBRA II HYPERBOLAS A HYPERBOLA CAN HAVE A  and if the transverse axis is vertical the vertices are located at ALGEBRA II HYPERBOLAS A HYPERBOLA CAN HAVE A 


The foci are very important and to locate them we need to find the distance from the center of the hyperbola to each focus. This distance is labeled c and we find it using the formula ALGEBRA II HYPERBOLAS A HYPERBOLA CAN HAVE A . Thus the foci will have coordinates ALGEBRA II HYPERBOLAS A HYPERBOLA CAN HAVE A  if the transverse axis is horizontal, and ALGEBRA II HYPERBOLAS A HYPERBOLA CAN HAVE A  if the axis is vertical. Most of the time c is an irrational number such as ALGEBRA II HYPERBOLAS A HYPERBOLA CAN HAVE A  . While it is perfectly fine to label the coordinates of the foci as ALGEBRA II HYPERBOLAS A HYPERBOLA CAN HAVE A  for example, to locate them on a graph a decimal approximation is necessary.


Hyperbolas also have “invisible” lines that they approach called asymptotes. For a hyperbola that is centered at the origin, these lines will intersect at the origin. There are two intersecting asymptotes and their equations will be ALGEBRA II HYPERBOLAS A HYPERBOLA CAN HAVE A  if the transverse axis is horizontal, and ALGEBRA II HYPERBOLAS A HYPERBOLA CAN HAVE A  if the transverse axis is vertical. Asymptotes MUST be sketched into the graph as dashed lines for the graph of a hyperbola to be correct and complete.




  1. ALGEBRA II HYPERBOLAS A HYPERBOLA CAN HAVE A 


  1. Where is the center:


  1. Is the transverse axis horizontal or vertical:



  1. What are the coordinates of the vertices:



  1. What are the equations of the asymptotes:



  1. What are the coordinates of the foci:



  1. Sketch the graph:



ALGEBRA II HYPERBOLAS A HYPERBOLA CAN HAVE A




  1. ALGEBRA II HYPERBOLAS A HYPERBOLA CAN HAVE A 


  1. Where is the center:


  1. Is the transverse axis vertical or horizontal:



  1. What are the coordinates of the vertices:



  1. What are the equations of the asymptotes:



  1. What are the coordinates of the foci:



  1. Sketch the graph:



ALGEBRA II HYPERBOLAS A HYPERBOLA CAN HAVE A










  1. ALGEBRA II HYPERBOLAS A HYPERBOLA CAN HAVE A 


  1. Where is the center:


  1. Is the transverse axis vertical or horizontal:



  1. What are the coordinates of the vertices:



  1. What are the equations of the asymptotes:



  1. Sketch the graph:



ALGEBRA II HYPERBOLAS A HYPERBOLA CAN HAVE A




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Tags: algebra ii, algebra, hyperbola, hyperbolas