A hyperbola centered at the origin has vertices at (0,+-sqrt19) and foci at (0,+-sqrt55). Write the equation of this hyperbola.

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A hyperbola centered at the origin has vertices at  (0,+-sqrt19) and foci at  (0,+-sqrt55). Write the equation of this hyperbola.

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Identify standard form: Identify the standard form of the equation for a hyperbola with a vertical transverse axis. Standard form of equation for a hyperbola with a vertical transverse axis:  (y-k)^2/a^2 - (x-h)^2/b^2 = 1Determine center: Determine the values of h and k, which represent 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. a is the distance from the center to a vertex along the y-axis. The vertices are given as (0, +-sqrt(19)), so a = sqrt(19).Find semi-minor axis: Find the value of the semi-minor axis b. The relationship between the semi-major axis a, the semi-minor axis b, and the distance c from the center to a focus is c^2 = a^2 + b^2. The foci are given as (0, +-sqrt(55)), so c = sqrt(55).Calculate value of b: Calculate the value of b using the relationship c^2 = a^2 + b^2. c^2 = (sqrt(55))^2 c^2 = 55 a^2 = (sqrt(19))^2 a^2 = 19 b^2 = c^2 - a^2 b^2 = 55 - 19 b^2 = 36 b = sqrt(36) b = 6Write equation in standard form: Write the equation of the hyperbola in standard form after substituting the values of h, k, a, and b. Substitute values of h, k, a, and b into (y-k)^2/a^2 - (x-h)^2/b^2 = 1. (y - 0)^2/(sqrt(19))^2 - (x - 0)^2/6^2 = 1 y^2/19 - x^2/36 = 1

A hyperbola centered at the origin has vertices at $(0, \pm \sqrt{19})$ and foci at $(0, \pm \sqrt{55})$ . $\newline$ Write the equation of this hyperbola.

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A hyperbola centered at the origin has vertices at (0,±19) (0, \pm \sqrt{19}) (0,±19​) and foci at (0,±55) (0, \pm \sqrt{55}) (0,±55​).\newlineWrite the equation of this hyperbola.

A hyperbola centered at the origin has vertices at $(0, \pm \sqrt{19})$ and foci at $(0, \pm \sqrt{55})$ . $\newline$ Write the equation of this hyperbola.