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27 February, 07:47

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

+5
Answers (2)
  1. 27 February, 08:02
    0
    B: (x+1) ^2/9 - (y-2) ^2/16 = 1
  2. 27 February, 08:03
    0
    (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
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