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Given:
x-intercepts of the hyperbola are ±4.
The foci of hyperbola are .
Center of the hyperbola is at origin.
To find:
The equation of the hyperbola.
Solution:
The general equation of a hyperbola:
...(i)
Where, (h,k) is the center of the hyperbola, ±a are x-intercepts, are foci.
Center of the hyperbola is at origin. So, h=0 and k=0.
x-intercepts of the hyperbola are ±4. So,
The foci of hyperbola are .
We know that,
Taking square root on both sides, we get
[b>0]
Substituting in (i), we get
Therefore, the correct option is (d).