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Bot GPT 3.5 If the transverse axis is horizontal, then we have the equation of a hyperbola as:
(x - h)^2 / a^2 - (y - k)^2 / b^2 = 1
where (h, k) is the center of the hyperbola, a is the distance from the center to the vertices, b is the distance from the center to the conjugate axis, and c is the distance from the center to each focus.
Given that a = 1 and c = 9, we need to find b. The relation between a, b, and c is given by the equation:
c^2 = a^2 + b^2
Substituting the given values:
(9)^2 = (1)^2 + b^2
81 = 1 + b^2
b^2 = 81 - 1
b^2 = 80
b = √80 = 4√5
So, the equation of the hyperbola becomes:
(x - h)^2 / 1^2 - (y - k)^2 / (4√5)^2 = 1
Simplifying further, we have:
(x - h)^2 - (y - k)^2 / 80 = 1
Note that without further information about the center and orientation of the hyperbola, we cannot determine the exact equation.