Question
Find the co-ordinates of foci, the vertices, the lenghts of transverse and conjugate axis, the eccentricity the length of latus rectum of hyperbola
Solution
The equation of hyperbola is :
which is of the form
∴ The foci and vertices lie on x-axis.
So,
∴
The co-ordinates of foci are:
The co-ordinates of the vertices are:
The length of transverse axis = 2a = 2 x 6 = 12
The length of conjugate axis = 2b = 2 x 8 = 16
Let the eccentricity be e, we know that c = ae 10 = 6e
The length of latus rectum