(i) Equation of the hyperbola:
This can be rewritten in the following way:
This is the standard equation of a hyperbola, where .
Coordinates of the foci are given by , i.e. .
Equation of directrices:
Length of the latus rectum of the hyperbola is .
Length of the latus rectum =
(ii) Equation of the hyperbola:
This can be rewritten in the following way:
This is the standard equation of a hyperbola, where .
Coordinates of foci are given by , i.e. .
Equation of the directrices:
Length of the latus rectum of the hyperbola =
Length of the latus rectum =
(iii) Equation of the hyperbola:
This can be rewritten in the following way:
This is the standard equation of a hyperbola, where .
Coordinates of the foci are given by , i.e. .
Equation of the directrices:
Length of the latus rectum of the hyperbola is .
(iv) Equation of the hyperbola:
This can be rewritten in the following way:
This is the standard equation of a hyperbola, where .
Coordinates of the foci are given by , i.e. .
Equation of the directrices:
Length of the latus rectum of the hyperbola =
(v) Equation of the hyperbola:
This can be rewritten in the following manner:
This is the standard equation of a hyperbola, where .
Coordinates of the foci are given by , i.e. .
Equation of the directrices:
Length of the latus rectum of the hyperbola is .