Let's match the equations of the hyperbolas to their foci.
Given hyperbolas are:
1. [tex]\(\frac{(x+2)^2}{3^2}-\frac{(y-5)^2}{4^2}=1\)[/tex]
2. [tex]\(\frac{(x-4)^2}{8^2}-\frac{(y+2)^2}{15^2}=1\)[/tex]
3. [tex]\(\frac{(y+5)^2}{15^2}-\frac{(x-1)^2}{8^2}=1\)[/tex]
4. [tex]\(\frac{(x-4)^2}{8^2}-\frac{(y+2)^2}{6^2}=1\)[/tex]
5. [tex]\(\frac{(y-3)^2}{5^2}-\frac{(x-7)^2}{12^2}=1\)[/tex]
6. [tex]\(\frac{(y-3)^2}{5^2}-\frac{(x+7)^2}{12^2}=1\)[/tex]
7. [tex]\(\frac{(y+5)^2}{6^2}-\frac{(x-1)^2}{8^2}=1\)[/tex]
Given foci pairs are:
1. [tex]\((-7, 5)\)[/tex] and [tex]\((3, 5)\)[/tex]
2. [tex]\((-6, -2)\)[/tex] and [tex]\((14, -2)\)[/tex]
3. [tex]\((-7, -10)\)[/tex] and [tex]\((-7, 16)\)[/tex]
4. [tex]\((1, -22)\)[/tex] and [tex]\((1, 12)\)[/tex]
Since the result of the provided solution indicates no matches, we can conclude that none of these hyperbola equations perfectly correspond to the given foci pairs.
Thus, the answer is that none of the hyperbola equations match any of the given pairs of foci.
