Q. 5 C5.0( 1 Vote )

# Find the centre, eccentricity, foci and directions of the hyperbola

x^{2} – 3y^{2} – 2x = 8

Answer :

**Given:** x^{2} – 3y^{2} – 2x = 8

**To find:** center, eccentricity(e), coordinates of the foci f(m,n), equation of directrix.

x^{2} – 3y^{2} – 2x = 8

⇒ x^{2} – 2x + 1 – 3y^{2} – 1 = 8

⇒ (x – 1)^{2} – 3y^{2} = 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:

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