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: