Hyperbola

A hyperbola is defined as the locus of points such that the difference between the distances to the two foci is constant. It is the conic section formed by slicing two cones such that the plane of the cut never intersects the center line of the cones.

$\frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2} = 1$ is the standard form of a horizontally opening hyperbola, while $\frac{(y-k)^2}{b^2}-\frac{(x-h)^2}{a^2} = 1$ is the standard form of a vertically opening one. Also, $xy=k$ for some real number $k$ is a hyperbola.

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Hyperbola