In the Hyperbola Module, you learned that the standard equations of a hyperbola centred at the origin are:
x2 | - | y2 | = 1
| or |
- |
x2 |
+ |
y2 |
= 1 |
a2 |
b2 |
a2 |
b2
|
depending on whether the vertices lie on the horizontal or vertical axes.
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As with circles and ellipses, hyperbolas can be descibed as a locus of points satisfying some special condition. This special condition for hyperbolas is that the difference of the distances between a point P on the hyperbola, and two fixed points F1 and F2 is constant.
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The two fixed points, F1 and F2 are again called the focal points or foci of the hyperbola.
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Notice that the locus definition of hyperbola is very similar to that of ellipses, with hyperbolas having a constant difference property, and ellipses having a constant sum property. |