One focus of a hyperbola is located at (-6, 2). One vertex of the hyperbola is located at (-4, 2). The center is (-1, 2).

What is the equation of the hyperbola?

= 1

= 1

= 1

= 1

B: (x+1) ^2/9 - (y-2) ^2/16 = 1

(x+1) ^2/9 - (y-2) ^2/16 = 1

Step-by-step explanation:

As the center and the vertex of the hyperbola forms a horizontal segment (they have the same y value), we can use the hyperbola equation with horizontal axis:

(x-h) ^2/a^2 - (y-k) ^2/b^2 = 1

For this equation, the center of the hyperbola is (h, k), the vertix is (h±a, k) and the focus is (h±c, k), where c^2 = a^2 + b^2

So if the center is (-1,2), we have h = - 1 and k = 2

If the vertex is (-4,2), we have that h-a = - 4, so a = 3

If the focus is (-6,2), we have that h-c = - 6, so c = 5

Now, finding b, we have:

5^2 = 3^2 + b^2

b = 4

So our equation is:

(x+1) ^2/9 - (y-2) ^2/16 = 1