Centre not at the origin
Hyperbola  |
Conjugate hyperbola |
 |
 |
| 1. Transverse axis is along y = k, Length of the transverse axis is 2a |
Transverse axis is along x = h, Length of the transverse axis is 2b |
| 2. Conjugate axis is along x = h, Length of conjugate axis is 2b |
Conjugate axis is along y = k, Length of conjugate axis is 2a |
| 3. Coordinates of the centre (h, k) | Coordinates of the centre (h, k) |
| 4. Coordinates of the foci (h ± ae, k) | Coordinates of the foci (h, k ± be) |
| 5. Equation of the directrices x = h ± a/e | Equation of the directrices y = k ± b/e |
6. Eccentricity e =  |
Eccentricity e' =  |