Question

The following hyperbola has a horizontal transverse axis: (x + 2) (w+7)=11617

Answer 1

for the given hyperbola

`((x+2)^2)/(16)-((y+7)^2)/(17)=1`

We have the following graph. Visually we can see that this hyperbola does have a transverse axis, however you can do all the calculations to check it

`\begin{gathered} ((x-h)^2)/(a^2)-((y-k)^2)/(b^2)=1 \\ h=-2 \\ k=-7 \\ a^2=16 \\ b^2=17 \\ c^2=16+17 \\ c=\sqrt[]{33}=5.7 \\ f_1=(h-c,k) \\ f_1=(-2-5.7,-7) \\ f_2=(-7.7,-7) \\ f_2=(3.7,-7) \\ y=-7\to\text{ is the ecuation of the transversal axis} \end{gathered}`

As we can see y = -7 is a line parallel to the x axis, turning the transversal axis horizontal.

That is, this hyperbola does have a horizontal transverse axis and the answer is TRUE