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Hyperbolas

Hyperbolas. Topic 7.5. Definitions. Hyperbola: set of all points where the absolute value of the difference of the distance from any point on the hyperbola to the foci is contant. Two Standard Equations. Vertical Hyperbola: Foci: Vertices: Asymptote Slopes:. Two Standard Equations.

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Hyperbolas

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  1. Hyperbolas Topic 7.5

  2. Definitions • Hyperbola: set of all points where the absolute value of the difference of the distance from any point on the hyperbola to the foci is contant

  3. Two Standard Equations • Vertical Hyperbola: • Foci: • Vertices: • Asymptote Slopes:

  4. Two Standard Equations • Horizontal Hyperbola: • Foci: • Vertices: • Asymptote Slopes:

  5. Writing in Standard Form • Complete the square for both the x-terms and y-terms and move the constant to the other side of the equation The first term will be the positive term between x2 and y2 • Divide all terms by the constant

  6. Example: Group terms Complete the square Simplify Don’t forget to the negative nine! Divide by Constant

  7. Graphing the hyperbola • Put equation in standard form • Graph the center (h, k) • Graph the foci (look at the equation to determine your direction) • Graph the vertices • Graph the asymptotes (start at the center and use “Rise over Run”) • Draw “U” shapes that go through the vertices and stay in between the asymptotes

  8. Example: 1) Graph Center 2) Graph Foci 3) Graph Vertices 4) Graph Asymptotes 5) Graph Hyperbola

  9. You Try!Write the following equation in standard form, then graph it.

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