(i) The centre of the hyperbola is the midpoint of the line joining the two focii.
So, the coordinates of the centre are .
Let 2a and 2b be the length of the transverse and conjugate axis and let e be the eccentricity.
Distance between the two focii = 2ae
Equation of the hyperbola is given below:
(ii) The centre of the hyperbola is given below:
If the other focus is , then it is calculated in the following way:
Thus, the other focus is .
Distance between the foci:
Equation of the hyperbola is given below:
(iii) The centre of the hyperbola is the midpoint of the line joining the two focii.
So, the coordinates of the centre are .
Let 2a and 2b be the length of the transverse and conjugate axis. Let e be the eccentricity.
Distance between the two focii = 2ae
Equation of the hyperbola:
(iv) The Vertices of the hyperbola are .
∴
The foci is .
∴
Therefore, the equation of the hyperbola is.