Hyperbola
hyperbola centered at (0,0)
OPENS LEFT AND RIGHT Horizontal Transverse Axis Equation y = 0 Length 2a Vertical Conjugate Axis Equation x = 0 Length 2b Asymptotes y = +(b/a)x Corners of "Box" (a,b) (-a,b) (-a,-b) (a, -b) Vertices ( a,0) (-a,0) Foci (c, 0) and (-c,0) |
hyperbola centered at (h,k)
OPENS LEFT AND RIGHT Horizontal Transverse Axis Equation y = k Length 2a Vertical Conjugate Axis Equation x = k Length 2b Asymptotes y = +(b/a)(x-h)+k Corners of "Box" (h+a,k+b) (h-a,k+b) (h-a,k-b) (h+a, k-b) Vertices ( h+a,k) (h-a,k) Foci (h+c, k) and (h-c,k) |
hyperbola centered at (0,0)
OPENS UP AND DOWN Vertical Transverse Axis Equation x = 0 Length 2b Horizontal Conjugate Axis Equation y = 0 Length 2a Asymptotes y = +(b/a)x Corners of "Box" (a,b) (-a,b) (-a,-b) (a, -b) Vertices ( 0,b) (0,b) Foci (o, c) and (0,-c) |
hyperbola centered at (h,k)
OPENS UP AND DOWN Vertical Transverse Axis Equation x = h Length 2b Horizontal Conjugate Axis Equation y = k Length 2a Asymptotes y = +(b/a)(x-h)+k Corners of "Box" (h+a,k+b) (h-a,k+b) (h-a,k-b) (h+a, k-b) Vertices ( h,k+b) (h,k-b) Foci (h, k+c) and (h,k-c) |