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