Answer
[tex]\frac{(x+8)^2}{4^{}}-\frac{(y-4)^2}{36^{}}=1[/tex]
Explanation
Since the transverse axis is parallel to the x-axis, this hyperbola opens left/right.
Coordinate of the center, (h, k) = (-8, 4)
The length of the transverse axis = 4 units. This implies that,
a = 4/2 = 2 and b = 12/2 = 6
Please note that the equation of a hyperbola is
[tex]\frac{\mleft(x-h\mright)^2}{a^2}-\frac{(y-k)^2}{b^2}=1[/tex]
This implies
[tex]\begin{gathered} \frac{\mleft(x--8\mright)^2}{2^2}-\frac{(y-4)^2}{6^2}=1 \\ \frac{(x+8)^2}{4^{}}-\frac{(y-4)^2}{36^{}}=1 \end{gathered}[/tex]
