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A hyperbola's orientation can be determined by its standard equation. If the equation is in the form ((y-k)^2/a^2 - (x-h)^2/b^2 = 1), the hyperbola opens vertically, while if it is in the form ((x-h)^2/a^2 - (y-k)^2/b^2 = 1), it opens horizontally. The center ((h, k)) is the midpoint between the vertices, which also helps in visualizing the hyperbola's direction. Additionally, the placement of the squared terms indicates the direction of the branches.

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3w ago

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