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### Vocabulary

##### Complete the chart.

Word | Definition |

Hyperbola | ________________________________________________________________ |

________________ | a shape is so large that no circle, no matter how large, can enclose the shape |

________________ | a line which a curve approaches as the curve and the line approach infinity |

Perpendicular hyperbola | ________________________________________________________________ |

### Hyperbolas

Hyperbolas two foci, and they can be defined as the set of points in a plane whose distances to these two points have the same *difference *. So in the picture below, for every point on the hyperbola, for some constant .

What is the general form for a hyperbola that opens upwards and downwards and whose foci lie on the axis? ___________________________

What is the shifted equation for a hyperbola that is centered around the point opening up and down? ___________________________

Left and right? ___________________________

.

**Sketch the Hyperbolas:**

**Identify the equation of the hyperbola using the image:**

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**Asymtotes**

For a hyperbola of the form , which lines are the asymtotes?

_______________________ _______________________

What about the form ?

_______________________ _______________________

.

**Find the equations of the asymptotes:**

**Graph the hyperbolas, give the equation of the asymptotes, use the asymptotes to enhance the accuracy of your graph.**

**.**

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