Find the centre, eccentricity, foci and directions of the hyperbola
x2 – y2 + 4x = 0
Given: x2 – y2 + 4x = 0
To find: center, eccentricity(e), coordinates of the foci f(m,n), equation of directrix.
x2 – y2 + 4x = 0
⇒ x2 + 4x + 4 – y2 – 4 = 0
⇒ (x + 2)2 – y2 = 4
Here, center of the hyperbola is (2, 0)
Let x – 2 = X
Formula used:
For hyperbola
Eccentricity(e) is given by,
Foci are given by (±ae, 0)
The equation of directrix are
Length of latus rectum is
Here, a = 2 and b = 2
Therefore,
⇒ and y = 0
⇒ and y = 0
⇒ and y = 0
Equation of directrix are: