Q12 of 71 Page 27

If the distance between the foci of a hyperbola is 16 and its eccentricity is, then obtain its equation.

Given: Distance between foci is 16 and eccentricity is


To find: equation of the hyperbola


Formula used:


The standard form of the equation of the hyperbola is,



The distance between foci is given by 2ae


According to question:


2ae = 16






⇒ a2 = 32


We know,


b2 = a2(e2 – 1)




⇒ b2 = 32


Hence, the equation of the hyperbola is:




⇒ x2 – y2 = 32


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