5.4 Hyperbolas (part 1) 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.

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Presentation transcript:

5.4 Hyperbolas (part 1) 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. Doted lines are not part of the graph

(Just the Slope, a = Vertices, b = Co-Vertices) 5.4 Hyperbolas Transverse axis Conjugate Axis Vertices Co-vertices Center Foci Asymptotes (2a) length of V1 to V2 (2b) length of CV1 to CV2 Endpoints of TA Endpoints of CA Intersection of the 2 axes Lie on inside of hyperbola & on TA Horizontal Vertical (Just the Slope, a = Vertices, b = Co-Vertices)

5.4 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

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.

Example 2: Write the standard equation of the hyperbola with V(-7, 0) (7, 0) and CV (0,-4) (0, 4).

Homework Worksheet 5.4