Section 10.4 Last Updated: December 2, 2007. Hyperbola  The set of all points in a plane whose differences of the distances from two fixed points (foci)

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Presentation transcript:

Section 10.4 Last Updated: December 2, 2007

Hyperbola  The set of all points in a plane whose differences of the distances from two fixed points (foci) are constant.

Equation of a Hyperbola Co-vertices endpoints of conjugate axis Center: (h, k)

Equation of a Hyperbola Co-vertices endpoints of conjugate axis

Hyperbola b 2 = c 2 - a 2

Graph the following Hyperbola Center: (-1, 5) a = 4 in horiz direction b = 7 in vertical direction

Graph the following Hyperbola Center: (-1, 5) a = 4 b = 7 b 2 = c 2 - a = c = c 2 49= c 2 -16

Graph the following Hyperbola Asymptotes

Graph the following Hyperbola Asymptotes

Graph the following Hyperbola Asymptotes Center: (-1, 5) Vertices: (-5, 5) (3, 5) Co-Vertices: (-1, 12) (-1, -2) Length of Transverse axis: 8 Length of Conjugate axis: 14 Foci:

Graph the following Hyperbola Center: (-2, 3) a = 6 in vertical direction b = 3 in horiz direction

Graph the following Hyperbola Center: (-2, 3) a = 6 b = 3 b 2 = c 2 - a = c = c 2 9 = c 2 -36

Graph the following Hyperbola Asymptotes

Graph the following Hyperbola Asymptotes

Graph the following Hyperbola Asymptotes Center: (-2, 3) Vertices: (-2, -3) (-2, 9) Co-Vertices: (-5, 3) (1, 3) Length of Transverse axis: 12 Length of Conjugate axis: 6 Foci:

Graph the following Hyperbola Center: (-1, 3) a = 6 in x direction b = 4 in y direction

Graph the following Hyperbola Center: (-1, 3) a = 6 b = 4 b 2 = c 2 - a = c = c 2 16 = c 2 -36

Graph the following Hyperbola Asymptotes

Graph the following Hyperbola Asymptotes

Graph the following Hyperbola Asymptotes: Center: (-1, 3) Vertices: (-7, 3) (5, 3) Co-Vertices: (-1, 7) (-1, -1) Length of Transverse axis: 12 Length of Conjugate axis: 8 Foci: