File:Ellipse Properties of Directrix and String Construction.svg
Summary
A diagram showing some basic properties of an <a href="https://en.wikipedia.org/wiki/ellipse" class="extiw" title="en:ellipse">ellipse</a>, including
*The distance to a focus, F, from the centre C, is the eccentricity, e multiplied by the semimajor axis, a. *The distance from one focus to the other via any point on the ellipse, P, is always 2a. *The distance from a point, P, on the ellipse to a focus is always proportional to the distance to a vertical line, D, called the directrix. The constant of proportionality is the eccentricity, e. *The eccentricity is always between 0 and 1. At zero, the ellispe becomes a circle, at 1 the ellipse becomes a parabola. Greater than one, it is a hyperbola.
Ellipse properties> e=0.8 , a=170 px , b=102 px , f=e*a=136 px , d=a/e=212.5 px , Origin = (0 px,0 px)
Other related images
<a href="//commons.wikimedia.org/wiki/File:Ellipse_Properties_Showing_Construction_with_string.svg" class="image"><img alt="Ellipse Properties Showing Construction with string.svg" src="https://upload.wikimedia.org/wikipedia/commons/thumb/d/d8/Ellipse_Properties_Showing_Construction_with_string.svg/150px-Ellipse_Properties_Showing_Construction_with_string.svg.png" width="150" height="110" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/d/d8/Ellipse_Properties_Showing_Construction_with_string.svg/225px-Ellipse_Properties_Showing_Construction_with_string.svg.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/d/d8/Ellipse_Properties_Showing_Construction_with_string.svg/300px-Ellipse_Properties_Showing_Construction_with_string.svg.png 2x" data-file-width="361" data-file-height="265"></a> <a href="//commons.wikimedia.org/wiki/File:Ellipse_Properties_of_Directrix.svg" class="image"><img alt="Ellipse Properties of Directrix.svg" src="https://upload.wikimedia.org/wikipedia/commons/thumb/6/62/Ellipse_Properties_of_Directrix.svg/150px-Ellipse_Properties_of_Directrix.svg.png" width="150" height="82" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/6/62/Ellipse_Properties_of_Directrix.svg/225px-Ellipse_Properties_of_Directrix.svg.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/6/62/Ellipse_Properties_of_Directrix.svg/300px-Ellipse_Properties_of_Directrix.svg.png 2x" data-file-width="884" data-file-height="484"></a>
These images were edited with the free open source program <a href="https://en.wikipedia.org/wiki/en:Inkscape" class="extiw" title="w:en:Inkscape">Inkscape</a>
Licensing
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File history
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 17:40, 5 January 2017 | | 884 × 484 (2 KB) | 127.0.0.1 (talk) | A diagram showing some basic properties of an <a href="https://en.wikipedia.org/wiki/ellipse" class="extiw" title="en:ellipse">ellipse</a>, including<br> *The distance to a focus, <i>F</i>, from the centre <i>C</i>, is the eccentricity, <i>e</i> multiplied by the semimajor axis, <i>a</i>. *The distance from one focus to the other via any point on the ellipse, <i>P</i>, is always 2<i>a</i>. *The distance from a point, <i>P</i>, on the ellipse to a focus is always proportional to the distance to a vertical line, <i>D</i>, called the directrix. The constant of proportionality is the eccentricity, <i>e</i>. *The eccentricity is always between 0 and 1. At zero, the ellispe becomes a circle, at 1 the ellipse becomes a parabola. Greater than one, it is a hyperbola.<br><p>Ellipse properties> e=0.8 , a=170 px , b=102 px , f=e*a=136 px , d=a/e=212.5 px , Origin = (0 px,0 px) <br> Other related images <br><a href="//commons.wikimedia.org/wiki/File:Ellipse_Properties_Showing_Construction_with_string.svg" class="image"><img alt="Ellipse Properties Showing Construction with string.svg" src="https://upload.wikimedia.org/wikipedia/commons/thumb/d/d8/Ellipse_Properties_Showing_Construction_with_string.svg/150px-Ellipse_Properties_Showing_Construction_with_string.svg.png" width="150" height="110" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/d/d8/Ellipse_Properties_Showing_Construction_with_string.svg/225px-Ellipse_Properties_Showing_Construction_with_string.svg.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/d/d8/Ellipse_Properties_Showing_Construction_with_string.svg/300px-Ellipse_Properties_Showing_Construction_with_string.svg.png 2x" data-file-width="361" data-file-height="265"></a> <a href="//commons.wikimedia.org/wiki/File:Ellipse_Properties_of_Directrix.svg" class="image"><img alt="Ellipse Properties of Directrix.svg" src="https://upload.wikimedia.org/wikipedia/commons/thumb/6/62/Ellipse_Properties_of_Directrix.svg/150px-Ellipse_Properties_of_Directrix.svg.png" width="150" height="82" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/6/62/Ellipse_Properties_of_Directrix.svg/225px-Ellipse_Properties_of_Directrix.svg.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/6/62/Ellipse_Properties_of_Directrix.svg/300px-Ellipse_Properties_of_Directrix.svg.png 2x" data-file-width="884" data-file-height="484"></a> </p> <br> These images were edited with the free open source program <a href="https://en.wikipedia.org/wiki/en:Inkscape" class="extiw" title="w:en:Inkscape">Inkscape</a> |
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