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GXWeb Ellipse
Saltire Software, home of Geometry Expressions and GXWeb
GXWeb Curve Construction Collection (like this one!)
About the Ellipse (from Wolfram MathWorld)
The Ellipse is a plane curve surrounding two focal points (A and D), such that for all points on the curve, the sum of the two distances to the focal points is a constant.
The hyperbola and the ellipse are closely related conics - can you see the values for a and f in this model for which it switches from hyperbola to ellipse and back again? Use the model to explore and study the cartesian equation below.
| \(a\) | |||||
| 0 | 1 | 10 | |||
| \(f\) | |||||
| 0 | 0 | 10 | |||
| \(\theta\) | |||||
| 0 | 0 | 1.57 | |||
 | The Ellipse constructed here is the locus of point E where \(a = Length(AB) = Length(CD)\) \(2*f = Length(AD) = Length(BC)\) and \(angle(BAD) = \theta\). |
Cartesian equation: \[4·Y^2·a^2-a^4+4·a^2·f^2+X^2·(4·a^2-16·f^2)\]
Try this yourself with the tools below...
Construct your own Model with GXWeb
WolframAlpha: CAS+
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©2020 Compass Learning Technologies ← Live Mathematics on the Web ← GXWeb Curve Construction Collection ← GXWeb Ellipse