Q5 of 71 Page 27

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:









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