Answer:
C. (y + 3)²/64 - (x + 1)²/36 = 1
Step-by-step explanation:
I think your question missed key information, allow me to add in and hope it will fit the orginal one. Please have a look at the attached photo
My answer:
From the photo, the given information is:
As we know, the hyperbola has general equation for it is:
![\frac{(y-k)^{2} }{a^{2}}-\frac{(x-h)^{2} }{b^{2}}=1](https://tex.z-dn.net/?f=%5Cfrac%7B%28y-k%29%5E%7B2%7D%20%7D%7Ba%5E%7B2%7D%7D-%5Cfrac%7B%28x-h%29%5E%7B2%7D%20%7D%7Bb%5E%7B2%7D%7D%3D1)
where h and k are the coordinate for the center (h, k) and we only needed the center of the hyperbola to find our answer.
In this situation, we have:
![\frac{(y-(-3))^{2} }{a^{2}}-\frac{(x-(-1))^{2} }{b^{2}}=1\\\frac{(y+3)^{2} }{a^{2}}-\frac{(x+1)^{2} }{b^{2}}=1](https://tex.z-dn.net/?f=%5Cfrac%7B%28y-%28-3%29%29%5E%7B2%7D%20%7D%7Ba%5E%7B2%7D%7D-%5Cfrac%7B%28x-%28-1%29%29%5E%7B2%7D%20%7D%7Bb%5E%7B2%7D%7D%3D1%5C%5C%5Cfrac%7B%28y%2B3%29%5E%7B2%7D%20%7D%7Ba%5E%7B2%7D%7D-%5Cfrac%7B%28x%2B1%29%5E%7B2%7D%20%7D%7Bb%5E%7B2%7D%7D%3D1)
Hence, we choose C.
Hope it will find you well.