Question

Which equation represents the hyperbola shown in the graph? A. x-3^2/64-y-1^2/36=1 B. x+3^2/64-y+1^2/36=1 C. y+1^2/64 - x+3^2/36=1 D. y-1^2/64 - x-3^2/36=1 ?

Answer 1

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:

• The vertex : (−1, 5).

• The center is (−1, −3).

As we know, the hyperbola has general equation for it is:

$\frac{(y-k)^{2} }{a^{2}}-\frac{(x-h)^{2} }{b^{2}}=1$

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:

$\frac{(y-(-3))^{2} }{a^{2}}-\frac{(x-(-1))^{2} }{b^{2}}=1\\\frac{(y+3)^{2} }{a^{2}}-\frac{(x+1)^{2} }{b^{2}}=1$

Hence, we choose C.

Hope it will find you well.