SOLUTION
From the question, the center of the hyperbola is
[tex]\begin{gathered} (h,k),\text{ which is } \\ (0,0) \end{gathered}[/tex]
a is the distance between the center to vertex, which is -1 or 1, and
c is the distance between the center to foci, which is -2 or 2.
b is given as
[tex]\begin{gathered} b^2=c^2-a^2 \\ b^2=2^2-1^2 \\ b=\sqrt[]{3} \end{gathered}[/tex]
But equation of a hyperbola is given as
[tex]\frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1[/tex]
Substituting the values of a, b, h and k, we have
[tex]\begin{gathered} \frac{(x-0)^2}{1^2}-\frac{(y-0)^2}{\sqrt[]{3}^2}=1 \\ \frac{x^2}{1}-\frac{y^2}{3}=1 \end{gathered}[/tex]
Hence the answer is
[tex]\frac{x^2}{1}-\frac{y^2}{3}=1[/tex]
