Question

I need help solving this practice problem Thank you in advance

Answer 1

`\frac{(x+8)^2}{4^{}}-\frac{(y-4)^2}{36^{}}=1`

Step-by-step 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

`(\mleft(x-h\mright)^2)/(a^2)-((y-k)^2)/(b^2)=1`

This implies

`\begin{gathered} (\mleft(x--8\mright)^2)/(2^2)-((y-4)^2)/(6^2)=1 \\ \frac{(x+8)^2}{4^{}}-\frac{(y-4)^2}{36^{}}=1 \end{gathered}`