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9.5 Hyperbolas Definition: A hyperbola is the set of points P(x,y) in a plane such that the absolute value of the difference between the distances from P to two fixed points in the plane, F1 and F2, called the foci, is a constant.

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**9.5 Hyperbolas Transverse axis Conjugate Axis Vertices Co-vertices**

Center Foci Asymptotes (2a) length of V to V (2b) length of CV to CV Endpoints of TA Endpoints of CA Intersection of the 2 axes Lie on inside of hyperbola Horizontal Vertical (When centered at the origin)

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9.5 Hyperbolas Notes: a2 is always the denominator of the ________ term when the equation is written in standard form. _________ axis can be longer or ____________ The length of the transverse axis is _________ The length of the conjugate axis is _________ a2 + b2 = c2 1st Either shorter 2a 2b

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a2 always comes 1st!

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Example 1: Write the standard equation of the hyperbola with vertices (-4,0) and (4,0) and co-vertices (0, -3) and (0, 3). Sketch the graph.

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Example 2: Write the standard equation of the hyperbola with V (0,-4) (0, 4) and CV(-7, 0) (7, 0) V: CV: Foci: a= b= c= Center:

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Example 5: Find the equation of the asymptotes and the coordinates of the vertices for the graph of Then graph the hyperbola. V: CV: Foci: a= b= c= Center:

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11.3 The Hyperbola. Hyperbola: the set of all points P in a plane such that the absolute value of the difference of the distances from two fixed points.

11.3 The Hyperbola. Hyperbola: the set of all points P in a plane such that the absolute value of the difference of the distances from two fixed points.

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