Objective: Graphing hyperbolas centered at the origin.

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Presentation transcript:

Objective: Graphing hyperbolas centered at the origin. Warm up Read the definition of a hyperbola. Write two facts about hyperbolas. Section 9.2, pg 886 Set of points in a plane, where the difference between any point and the foci is constant. Vertices are a units from the center.

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Example 1 Find the vertices and locate the foci for each hyperbola. a Example 1 Find the vertices and locate the foci for each hyperbola. a. b.

Example 2 Find the standard form of the equation of a hyperbola with foci at (0, -5) and (0, 5); vertices (0, -3) and (0, 3).

Steps for graphing a hyperbola: State whether the hyperbola has a vertical or horizontal transverse axis. Find a, b, and c. Plot center and count a, b, and c to plot vertices, co-vertices and foci. Draw boundary box and asymptotes. Draw both u-shapes at vertices. Example 3 Graph and locate the foci. Find equations of the asymptotes.

Example 4 Graph and locate the foci. Find equations of the asymptotes.

Classwork Gizmo: Hyperbola-Activity A. Pg 898 #4,14,22,24,28,30 Quiz on Thursday: 9.1-9.2 Graphing ellipses. Writing equations in standard form Graphing hyperbolas.