Question

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

Answer 1

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

Explanation:

Answer 2

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

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