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1. The hyperbola centered at the origin’s equation that complies with the requirements is x²/9 – y²/25 = 1.

   The hyperbola has a horizontal transverse axis because it has x-intercepts.

   The equation for a hyperbola with a horizontal transverse axis has the following standard form:

   (x – h)²/a² – (y – k)²/b² = 1.

   There is a center at (h,k).

   The vertices are separated by a distance of 2a.

   a and b have values of;

   2a = x₂ – x₁ = 3 – (-3) = 3 + 3 = 6 for “a,” and a = 6/2 = 3 and b = 5.

   The hyperbola’s equation, with its center at the origin, that meets the requirements is;

   (x – h)²/a² – (y – k)²/b² = 1,

   or, (x – 0)²/3² – (y – 0)²/5² = 1,

   or, x²/9 – y²/25 = 1.

   As a result, the hyperbola’s equation, centered at its origin, that fulfills the requirements is x²/9 – y²/25 = 1.

   Learn more about hyperbola equations at

   https://brainly.com/question/15624362

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   The provided question is incomplete. The complete question is:

   “Find the equation of the hyperbola centered at the origin that satisfies the given conditions: x-intercepts = +,-3 and asymptote at y=5/3x”

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