Q5 of 71 Page 27

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:









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