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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