Answer:
C. (y + 3)²/64 - (x + 1)²/36 = 1
Step-by-step explanation:
This is a hyperbola with a vertically tranversed axis, so the general equation for it is:
[tex]\frac{(y-k)^{2} }{a^{2}}-\frac{(x-h)^{2} }{b^{2}}=1[/tex]
where h and k are the coordinate for the center (h, k)
we're given center is (−1, −3), so
h = -1
k = -3
[tex]\frac{(y-(-3))^{2} }{a^{2}}-\frac{(x-(-1))^{2} }{b^{2}}=1[/tex]
[tex]\frac{(y+3)^{2} }{a^{2}}-\frac{(x+1)^{2} }{b^{2}}=1[/tex]
The information about "One focus of a hyperbola is located at (−1, 7). One vertex of the hyperbola is located at (−1, 5)" are irrelevant because the a and b values are the same for all the answers. So we literally only needed the center of the hyperbola to find our answer.
The only answer with (y+3) and (x+1) is C.
