Rectangular Hyperbola With Horizontal/vertical Asymptotes (Cartesian Coordinates)
Rectangular hyperbolas with the coordinate axes parallel to their asymptotes have the equation
- .
These are equilateral hyperbolas (eccentricity ) with semi-major axis and semi-minor axis given by .
The simplest example of rectangular hyperbolas occurs when the center (h, k) is at the origin:
describing quantities x and y that are inversely proportional. By rotating the coordinate axes counterclockwise by 45 degrees, with the new coordinate axes labelled the equation of the hyperbola is given by canonical form
- .
Read more about this topic: Hyperbola
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