9.5. Hyperbolas http://www.ck12.org
9.5 Hyperbolas
Here you will translate conic equations into graphing form and graph hyperbolas. You will also learn how to
measure the eccentricity of a hyperbola and solve word problems.
Hyperbolas are relations that have asymptotes. When graphing rational functions you often produce a hyperbola. In
this concept, hyperbolas will not be oriented in the same way as with rational functions, but the basic shape of a
hyperbola will still be there.
Hyperbolas can be oriented so that they open side to side or up and down. One of the most common mistakes that
you can make is to forget which way a given hyperbola should open. What are some strategies to help?
Watch This
MEDIA
Click image to the left for use the URL below.
URL: http://www.ck12.org/flx/render/embeddedobject/61869http://www.youtube.com/watch?v=i6vM82SNAUk James Sousa: Conic Sections: The Hyperbola part 1
MEDIA
Click image to the left for use the URL below.
URL: http://www.ck12.org/flx/render/embeddedobject/61871http://www.youtube.com/watch?v=6Xahrwp6LkI James Sousa: Conic Sections: The Hyperbola part 2
Guidance
A hyperbola has two foci. For every point on the hyperbola, the difference of the distances to each foci is con-
stant. This is what defines a hyperbola. The graphing form of a hyperbola that opens side to side is:
(x−a 2 h)^2 −(y−b 2 k)^2 = 1
A hyperbola that opens up and down is:
(y−a 2 k)^2 −(x−b 2 h)^2 = 1
Notice that for hyperbolas, agoes with the positive term andbgoes with the negative term. It does not matter
which constant is larger.