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The Hyperbola Horizontal Hyperbola: Standard Forms of Hyperbolas: ( x -h) ( v-k ) Vertical Hyperbola: = 1 ( v-k) ( x-h ) a2 =1 b Vertices: (hta, k) Vertices: (h, k + a) Asymptotes: (v-k) =+(x-h) Asymptotes: (y-k) =+ (x-h) Foci: (h+c,k) Foci: (h, k + c) Graph each hyperbola and identify the vertices, the location of its foci, and the equations of its asymptotes. 1) 9x2 -16v2 = 144 2) ' - 25x2 =25 25 25 Vertices: Vertices: Foci: Foci: Asymptotes: Asymptotes: 3) ( x - 2)2 (v + 2 )2-1 4) (1-2 ) (x+ 3) 4 16 4 9 Vertices: Vertices: Foci: Foci: ( 4 Asymptotes: Asymptotes:5) Write an equation of the hyperbola with foci at (0, 45) and vertices at (0, +3). 6) Write an equation of the hyperbola with foci at (3+ V10,3 ) and vertices at (4,3) and (2,3). 7) Write an equation of the hyperbola with foci at (4,5) and (4,-3) and vertices at (4,4) and (4,-2). 8) Write the equation in standard form. 9) Write the equation in standard form. 4x2 - 12 - 16x-4y-4=0 -9x2 + 1632 +54x+64y-161=0