The equation to the hyperbola having its eccentricity 2 and the distance between its foci is 8, is,
In the standard hyperbola,
x2a2 − y2b2 = 1
Given that eccentricity,
e=2
Also distance between the foci is given by 2ae.
Given,
2ae=8
i.e.,ae=4
∴ a=4e = 2
The lengths of transverse axis,conjugate axis and
the eccentricity are related by.
b2 = a2 (e2−1)
i.e.,b2=4.(4−1)
=12.
∴ The required equation of hyperbola is,
x24 − y212 = 1