Characteristic of different types of hyperbolas are given in the following table:

x^2/a^2 – y^2/b^2 = 1 
y^2/a^2 – x^2/b^2 =1 
Transverse axis 
x axis 
y axis 
Conjugate axis 
y axis 
x axis 
Equation of transverse axis 
Y =0 
X = 0 
Equation of conjugate axis 
X = 0 
Y = 0 
Length of transverse axis 
2 a unit 
2 a unit 
Length of conjugate axis 
2 b unit 
2 b unit 
Coordinates of Centre 
(0, 0) 
(0, 0) 
Coordinate of vertices 
(±a, 0) 
(0, ±a) 
Coordinates of foci 
(±a e, 0) 
(0, ±ae) 
Distance between two foci 
2 a e unit 
2 a e unit 
Length of latus rectum 
2 b^2 / a unit 
2 b^2 / a unit 
Equations of latera recta 
x = ±a e 
y = ±a e 
Equations of directrices 
x = ±a / e 
Y = ±a / e 
Distance between two directrices 
2 a / e unit 
2 a / e unit 
Question1:  Find the length of the latus rectum of the hyperbola
9 y ^2 – 4 x^2 = 36.
Solution:  9 y ^2 – 4 x^2 = 36
Or, y^2/4 – x^2/9 = 1
Comparing the above equation with the equation of hyperbola
y^2/a^2 – x^2/b^2 =1 we get,
A^2= 24, therefore a =2
And b^2=9, therefore b =3
Length of its latus rectum: 2 b^2 / a = 2*3^2 / 2 = 9.
Question 2:  For the same above parabola find the axes.
Solution: Transverse axis = 2a= 2*2=4
Conjugate axis = 2b= 2*3 = 6