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Hyperbola Equations and the Focal Property

Set of points in a plane whose distances to two foci have the same difference.

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Conic Sections: Hyperbolas

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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 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 pointP on the hyperbola, |d2d1|=C for some constant C .

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

What is the shifted equation for a hyperbola that is centered around the point (h,k) opening up and down? ___________________________    

Left and right? ___________________________


Sketch the Hyperbolas:

  1. y24(x1)24=9
  2. (x2)29(y+4)24=1
  3. (x3)29(y+1)216=1

Identify the equation of the hyperbola using the image:

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For a hyperbola of the form x2a2y2b2=1 , which lines are the asymtotes?

_______________________    _______________________

What about the form y2a2x2b2=1?

_______________________    _______________________


Find the equations of the asymptotes:

  1. (x1)219(y+4)21=9
  2. (y+2)216(x2)21=1
  3. (x4)21(y+1)24=1
  4. y216(x+1)24=1
Graph the hyperbolas, give the equation of the asymptotes, use the asymptotes to enhance the accuracy of your graph.
  1. (x2)216(y+4)21=1
  2. (x+2)29(y+2)216=1
  3. (x+4)29(y2)24=1


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