SimReal: Mathematics - Conic - Ellipse UiA Logo


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Ellipse

An ellipse with axis a and b and the center in origin can be described by the equation:
x2/a2 + y2/b2 = 1 or by the equation
x = acost
y = bsint

In this application the default ellipse is given by:
x = 8cost
y = 5sint

A point P on the ellipse and the two focus points F2 and F2 are shown.
You can move the point P along the ellipse
and change the eccentricity e of the ellipse by moving the focus points.

The tangent and the normal to the ellipse at point P can be shown.
The construction of the ellipse and the reflextion property of the ellipse can be studied.
Control objects  :
x = acost        : x-coordinate of a point P on the ellipse
y = bsint        : y-coordinate of a point P on the ellipse
tMin             : Start value of the parameter t 
tMax             : End   value of the parameter t
tCur             : Current parameter t of the ellipse pont P 
Path Total       : Show the whole ellipse
Path Current     : Show the ellipe up to the point P 
Ellipse Point    : Show the ellipse point P
Position Line    : Show the line from origin to the point P 
Focus Point      : Show the two focus points F1 and F2
Move Focus Point : Move the focus point by the scrollbar 
e =              : Show the eccentricity e = c/a 
Tangent          : Show the tangent at the elllipse point P 
Normal           : Show the normal at the ellipse point P 
Beam             : Show reflection property of the ellipse 
Axis             : Show the coordinate axis
Grid             : Show the grid
Txt              : Show the text of the points P, F1 and F2
Formula          : Show the formula of the ellipse
  

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