Q23 of 27 Page 11

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


As we know standard form of the equation of hyperbola is,



Distance between foci is given by 2ae


According to question:


2ae = 16



{∵e=√2}




⇒ a2 = 32


We know,


b2 = a2(e2 – 1)



⇒b2 =32(2-1)


⇒ b2 = 32


Hence, equation of hyperbola is:




⇒ x2 – y2 = 32


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