Given
The foci are given (6, -8) and (6, -14).
The vertices are given (6, -10) and (6,-12).
Explanation
To determine the equation of hyperbola ,
Use the general equation of hyperbola .
[tex]\frac{(y-k)^2}{b^2}-\frac{(x-h)^{2}}{a^{2}}=1[/tex]
The distance between foci is denoted as 2c.
[tex]\sqrt{(6-6)^2+(-14+8)^2}=\sqrt{36}=6[/tex][tex]\begin{gathered} 2c=6 \\ c=3 \end{gathered}[/tex]
The distance between vertices is denoted as 2a.
[tex]\sqrt{(6-6)^2+(-12+10)^2}=\sqrt{4}=2[/tex][tex]\begin{gathered} 2a=2 \\ a=1 \end{gathered}[/tex]
Now find the value of b,
[tex]\begin{gathered} c^2=a^2+b^2 \\ 3^2=1^2+b^2 \\ b^2=9-1 \\ b^2=8 \end{gathered}[/tex]
