Answer:
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
