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The equation for a hyperbola

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How do you find an equation for a hyperbola. Need list of steps taken to find an equation for a hyperbola. Solve the following to reinforce my understanding:

1) Vertices (+or-4, 0) and passing thru (8,3)
2) Foci (0,+-9)Center, directrices y = +-4
3) Center (1,-3), vertices (-4,3) and (2,3), foci (-6, 3) and (4,3)

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Solution Summary

The equation for a hyperbola is given. Vertices, foci and centers are determined.

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The equation for a hyperbola with semimajor axis parallel to the x-axis and semiminor axis parallel to the y-axis is given by

or, for a center at the point instead of ,

Unlike the ellipse, no points of the hyperbola actually lie on the semiminor axis, but rather the ratio ...

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