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9.5 Graph and Write Equations of Hyperbola

9.5 Graph and Write Equations of Hyperbola. A hyperbola is the set of all points, P , in a plane such that the difference of the distances between P and two fixed points, called the foci , is a constant. http://rowdy.mscd.edu/~talmanl/HTML/Hyperbola.html. Some Definitions:.

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9.5 Graph and Write Equations of Hyperbola

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  1. 9.5 Graph and Write Equations of Hyperbola

  2. A hyperbola is the set of all points, P, in a plane such that the difference of the distances between P and two fixed points, called the foci, is a constant. http://rowdy.mscd.edu/~talmanl/HTML/Hyperbola.html

  3. Some Definitions: Major Axis - Axis which runs through the center of the hyperbola, through the foci and has endpoints that are vertices. Minor Axis - Axis which runs through the center of the hyperbola and is perpendicular to the major axis. Vertices - Endpoints of the major axis that are each a units away from the center. The vertices are the vertices of the branches of the hyperbola. Co-Vertices - Endpoints that are each b units away from the center on the minor axis. Foci (plural of focus) – Two points along the major axis of a hyperbola that are c units away from the center. Asymptotes – Lines that intersect at the center of the hyperbola that represent limits on the branches of the hyperbola.

  4. Working with the Equations: Standard form of an equation of a hyperbola: Major axis is horizontal Major axis is vertical Helpful Hint: can be greater than, less than or equal to

  5. Finding the location of the foci: …where c is the distance of a focus point from the center of the hyperbola along the major axis.

  6. Let’s try working with hyperbolas: Graph and identify vertices, co-vertices and foci of the hyperbola. Put equation in standard form, if necessary Identify the center and graph Identify the vertices and graph Identify the co-vertices and graph Draw a rectangle through the vertices and co-vertices. Asymptotes are the diagonals of the rectangle. Identify the foci and graph Draw branches of the hyperbola

  7. Let’s try working with hyperbolas: Graph and identify vertices, co-vertices and foci of the hyperbola. Put equation in standard form, if necessary Identify the center and graph Identify the vertices and graph Identify the co-vertices and graph Draw a rectangle. Asymptotes are the diagonals of the rectangle. Identify the foci and graph Draw branches of the hyperbola

  8. Write equations of hyperbolas: Foci: (-3, 0) (3, 0) Vertices: (-1, 0) (1, 0) Vertices: (4, 2) (4, 8) Foci: (4, -2) (4, 12)

  9. Ultimate Parabola Challenge: • Work with your partner • Must graph the parent and translate. • Must put focus, directrix and axis of symmetry on the graph • Must list the parent function, vertex, focus, directrix and axis of symmetry separately • Must be able to explain your work

  10. Parent Function: _________________ Vertex: _________________________ Focus: _________________________ Directrix: ________________________ Axis of Symmetry: _________________

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