GXWeb Ellipse

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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 3 10

$f$

0 1 10

$\theta$

0 0.78 1.57

App generated by GXWeb

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: $4·Y^2·a^2-a^4+4·a^2·f^2+X^2·(4·a^2-16·f^2)$

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©2020 Compass Learning Technologies ← Live Mathematics on the Web ← GXWeb Curve Construction Collection ← GXWeb Ellipse