A hyperbola centered at the origin has vertices at (+-sqrt4,0) and foci at (+-sqrt9,0). Write the equation of this hyperbola.

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A hyperbola centered at the origin has vertices at  (+-sqrt4,0) and foci at  (+-sqrt9,0). Write the equation of this hyperbola.

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Identify standard form: Identify the standard form of the equation for a hyperbola centered at the origin with horizontal transverse axis. Standard form of equation for a hyperbola with horizontal transverse axis:  (x-h)^2/a^2 - (y-k)^2/b^2 = 1 where (h, k) is the center of the hyperbola.Determine center coordinates: Determine the values of h and k for the center of the hyperbola. Since the hyperbola is centered at the origin, h = 0 and k = 0.Find semi-major axis: Find the value of the semi-major axis a. The vertices are given at (±√4,0), which means a = √4 = 2.Find semi-minor axis: Find the value of the semi-minor axis b using the relationship c^2 = a^2 + b^2, where c is the distance from the center to a focus. The foci are given at (±√9,0), which means c = √9 = 3.Calculate value of b: Calculate the value of b using the relationship c^2 = a^2 + b^2. Substitute a = 2 and c = 3 into the equation to find b. 3^2 = 2^2 + b^2 9 = 4 + b^2 b^2 = 9 - 4 b^2 = 5 b = √5Write equation in standard form: Write the equation of the hyperbola in standard form after substituting the values of h, k, a, and b. Substitute h = 0, k = 0, a = 2, and b = √5 into (x-h)^2/a^2 - (y-k)^2/b^2 = 1. x^2/2^2 - y^2/(√5)^2 = 1 x^2/4 - y^2/5 = 1

A hyperbola centered at the origin has vertices at $( \pm \sqrt{4}, 0)$ and foci at $( \pm \sqrt{9}, 0)$ . $\newline$ Write the equation of this hyperbola.

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A hyperbola centered at the origin has vertices at (±4,0) ( \pm \sqrt{4}, 0) (±4​,0) and foci at (±9,0) ( \pm \sqrt{9}, 0) (±9​,0).\newlineWrite the equation of this hyperbola.

A hyperbola centered at the origin has vertices at $( \pm \sqrt{4}, 0)$ and foci at $( \pm \sqrt{9}, 0)$ . $\newline$ Write the equation of this hyperbola.