Respuesta :
From the given information, we can to note that the hyperbola is vertical, that is, it opens upwards (and downward for the other branch). Then, the possible solutions are option C and D and it has the form
[tex]\frac{(y-k)^2}{a^2}-\frac{(x-h)^2}{b^2}=1[/tex]where (h,k) corresponds to the center coordinates and a represents the distance from the center to the vertex. Then, from the given information, a is given by
[tex]a=7-4=3[/tex]So, our hyperbola has the form
[tex]\begin{gathered} \frac{(y-7)^2}{3^2}-\frac{(x-0)^2}{b^2}=1 \\ \end{gathered}[/tex]that is,
[tex]\frac{(y-7)^2}{9}-\frac{x^2}{b^2}=1[/tex]So by comparing this last result with the given options, we can to note that options D has the same "a" squared ( which is 9). Therefore, the answer is option D
