Hyperbola Last Updated: March 11, 2008.

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Presentation transcript:

hyperbola Last Updated: March 11, 2008

Hyperbola The set of all co-planar points whose difference of the distances from two fixed points (foci) are constant. foci foci

Co-vertices endpoints of conjugate axis Hyperbola Center: (h, k) conjugate axis vertex vertex transverse axis Co-vertices endpoints of conjugate axis

Co-vertices endpoints of conjugate axis Hyperbola vertex transverse axis Co-vertices endpoints of conjugate axis conjugate axis vertex

Hyperbola c2 = a2 + b2 Distance from center to vertex = a Distance from center to co-vertex = b Distance from center to foci = c b a c2 = a2 + b2 c

Graph the following Hyperbola Center: (-1, 5) a = 4 in x direction b = 7 in y direction (-1, 12) 7 (-1, 5) (-5, 5) 4 4 (3, 5) 7 (-1, -2)

Graph the following Hyperbola Center: (-1, 5) a = 4 b = 7 a2 + b2 = c2 (-1, 12) 42 + 72 = c2 16 + 49 = c2 65 = c2 7 foci (-1, 5) (-5, 5) 4 4 (3, 5) 8.1 = c 7 (-1, -2)

Graph the following Hyperbola Asymptotes (-1, 12) 7 (-1, 5) (-5, 5) 4 4 (3, 5) 7 (-1, -2)

Graph the following Hyperbola Asymptotes (-1, 12) 7 (-1, 5) (-5, 5) 4 4 (3, 5) 7 (-1, -2)

Graph the following Hyperbola Center: (-2, 3) a = 6 in y direction b = 3 in x direction (-2, 9) 6 (-2, 3) (-5, 3) 3 3 (1, 3) 6 (-2, -3)

Graph the following Hyperbola Center: (-2, 3) a = 6 b = 3 a2 + b2 = c2 (-2, 9) 62 + 32 = c2 36 + 9 = c2 45 = c2 6 foci (-2, 3) (-5, 3) 3 3 (1, 3) 6.7 = c 6 (-2, -3)

Graph the following Hyperbola Asymptotes (-2, 9) 6 (-2, 3) (-5, 3) 3 3 (1, 3) 6 (-2, -3)

Graph the following Hyperbola Asymptotes (-2, 9) 6 (-2, 3) (-5, 3) 3 3 (1, 3) 6 (-2, -3)

Graph the following Hyperbola Center: (-1, 3) a = 6 in x direction (-1, 7) b = 4 in y direction 4 (-1, 3) 6 6 (-7, 3) (5, 3) 4 (-1, -1)

Graph the following Hyperbola Center: (-1, 3) a = 6 b = 4 foci a2 + b2 = c2 (-1, 7) 62 + 42 = c2 36 + 16 = c2 4 52 = c2 (-1, 3) 6 6 (-7, 3) (5, 3) 4 (-1, -1)

Graph the following Hyperbola Asymptotes (-1, 7) 4 (-1, 3) 6 6 (-7, 3) (5, 3) 4 (-1, -1)

Graph the following Hyperbola Asymptotes (-1, 7) 4 (-1, 3) 6 6 (-7, 3) (5, 3) 4 (-1, -1)

Graph the following Hyperbola Center: (-2, 4) a = 2 in y direction b = 3 in x direction (-2, 6) 2 (-2, 4) 3 3 (-5, 4) (1, 4) 2 (-2, 2)

Graph the following Hyperbola Center: (-1, 3) a = 2 b = 3 a2 + b2 = c2 (-2, 6) 22 + 32 = c2 4 + 9 = c2 foci 13 = c2 2 (-2, 4) 3 3 (-5, 4) (1, 4) 2 (-2, 2)

Graph the following Hyperbola Asymptotes (-2, 6) 2 (-2, 4) 3 3 (-5, 4) (1, 4) 2 (-2, 2)

Graph the following Hyperbola Asymptotes (-2, 6) 2 (-2, 4) 3 3 (-5, 4) (1, 4) 2 (-2, 2)