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Transformations of a Hyperbola - Problem 3 413 views

Eventhough we are not explicitly asked to graph, it is useful to sketch the vertices and foci to determine the orientation of the hyperbola and visualize the center, which will be the midpoint. The distance from the center to a focus tells us "c", and from the center to a vertex tells us "a." Then we use the relationship a^2 + b^2 = c^2 to find b^2. Since the hyperbola axis is vertical, we know that the y^2 binomial will be first and over the a^2 term, and the x^2 binomial will be second and over the b^2 term. A hyperbola equation should always equal one.

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