The foci and the vertices of the hyperbola are labeled.
Which equation represents the hyperbola?

Correct option: first one -> (x+2)^2/64 - (y+4)^2/36 = 1

Step-by-step explanation:

The equation of the horizontal major axis hyperbola is:

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

The center is located at (h,k), the vertices are (h+a,k) and (h-a,k) and the focuses are (h+c, k) and (h-c, k)

In this case, the vertices are (-10,-4) and (6,-4), so we have k = -4.

To find h and a, we have:

h+a = 6

h-a = -10

summing both equations, we have:

2h = -4

h = -2

and then for 'a':

-2+a = 6

a = 8

The focus it two units away from the vertix, so c = a + 2, then c = 10

To find b, we can use the relation c^2 = a^2 +b^2:

10^2 = 8^2 + b^2

b^2 = 100 - 64 = 36

b = 6

So the equation of the hyperbola is:

(x+2)^2/64 - (y+4)^2/36 = 1

Correct option: first one

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step-by-step explanation:

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