Find the centre, eccentricity, foci and directions of the hyperbola
x2 – 3y2 – 2x = 8
Given: x2 – 3y2 – 2x = 8
To find: center, eccentricity(e), coordinates of the foci f(m,n), equation of directrix.
x2 – 3y2 – 2x = 8
⇒ x2 – 2x + 1 – 3y2 – 1 = 8
⇒ (x – 1)2 – 3y2 = 9
Here, center of the hyperbola is (1, 0)
Let x – 1 = X
Formula used:
For hyperbola
Eccentricity(e) is given by,
Foci is given by (±ae, 0)
Equation of directrix are:
Length of latus rectum is
Here, a = 3 and b =
Therefore,
⇒ and y = 0
⇒ and y = 0
⇒ and y = 0
Equation of directrix are: