Hyperbola Last Updated: October 11, 2005 Jeff Bivin -- LZHS.

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hyperbola Last Updated: October 11, 2005 Jeff Bivin -- LZHS

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

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

Co-vertices endpoints of conjugate axis Hyperbola vertex transverse axis Co-vertices endpoints of conjugate axis conjugate axis vertex Jeff Bivin -- LZHS

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 Length of transverse axis = 2a Length of conjugate axis = 2b

Hyperbola The Latus Rectum (LR) is a chord passing through the focus that is perpendicular to an extended transverse axis. The length of the L.R. is Distance from center to vertex = a Distance from center to co-vertex = b Distance from center to foci = c Jeff Bivin -- LZHS

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) Jeff Bivin -- LZHS

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) 7 (-1, -2) Jeff Bivin -- LZHS

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

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

Graph the following Hyperbola Find the Length of the LR. a = 4 b = 7 c = (-1, 12) 7 (-1, 5) (-5, 5) 4 4 (3, 5) 7 (-1, -2) Jeff Bivin -- LZHS

Graph the following Hyperbola Center: (-1, 5) Vertices: (-5, 5) (3, 5) Co-Vertices: (-1, 12) (-1, -2) Foci: (-1, 12) Length of Transverse axis: 8 Length of Conjugate axis: 14 7 (-1, 5) Asymptotes (-5, 5) 4 4 (3, 5) 7 (-1, -2) Jeff Bivin -- LZHS

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) Jeff Bivin -- LZHS

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 (-2, -3) Jeff Bivin -- LZHS

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

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

Graph the following Hyperbola Find the Length of the LR. a = 6 b = 3 c = (-2, 9) 6 (-2, 3) (-5, 3) 3 3 (1, 3) 6 (-2, -3) Jeff Bivin -- LZHS

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

Graph the following Hyperbola 4x2 + 8x - 9y2 + 54y - 53 = 168 (4x2 + 8x ) - (9y2 - 54y ) = 168 + 53 4(x2 + 2x + 12) - 9(y2 - 6y + 32) = 221 + 4 - 81 4(x + 1)2 - 9(y - 3)2 = 144 144 36 16 Jeff Bivin -- LZHS

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) (3, 5) 4 (-1, -1) Jeff Bivin -- LZHS

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) Jeff Bivin -- LZHS

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

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

Graph the following Hyperbola Find the Length of the LR. a = 6 b = 4 c = (-1, 7) 4 (-1, 3) 6 6 (-7, 3) (5, 3) 4 (-1, -1) Jeff Bivin -- LZHS

Graph the following Hyperbola Center: (-1, 3) Vertices: (-7, 3) (5, 3) Co-Vertices: (-1, 7) (-1, -1) Foci: (-1, 7) Length of Transverse axis: 12 Length of Conjugate axis: 8 4 (-1, 3) Asymptotes: 6 6 (-7, 3) (5, 3) 4 (-1, -1) Jeff Bivin -- LZHS

Graph the following Hyperbola 4x2 + 16x - 9y2 + 72y - 5 = 87 4x2 + 16x - 9y2 + 72y = 87 + 5 4(x2 + 4x + 22) - 9(y2 - 8y + (-4)2) = 92 + 16 - 144 4(x + 2)2 - 9(y - 4)2 = -36 -36 -9 4 Jeff Bivin -- LZHS

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) Jeff Bivin -- LZHS

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) Jeff Bivin -- LZHS

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

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

Graph the following Hyperbola Find the Length of the LR. a = 2 b = 3 c = (-2, 6) 2 (-2, 4) 3 3 (-5, 4) (1, 4) 2 (-2, 2) Jeff Bivin -- LZHS

Graph the following Hyperbola Center: (-2, 4) Vertices: (-2, 6) (-2, 2) Co-Vertices: (-5, 4) (1, 4) Foci: (-2, 6) Length of Transverse axis: 4 Length of Conjugate axis: 6 2 Asymptotes (-2, 4) 3 3 (-5, 4) (1, 4) 2 (-2, 2) Jeff Bivin -- LZHS

That's All Folks