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Ellipse – Conic Section – Educational Animations

Ellipse – conic section – educational animations

Ellipse

In mathematics, especially in geometry, ellipse is a conic curve, this means that it is formed with the points that simultaneously belong to a cone and to a plane that cut it off.

Below, you will see animations of various properties of the hyperbole, especially those that  differenciate it from the conic curve parable and hiperbole.

 

 

Ellipse – Conic section

Ellipse


When a right circular cone is sectioned by a plane oblique to the axis and forming with this axis an angle greater than the angle which the generatrix shape with the axis of the points belonging to both the plane and the cone form an ellipse.

Rule

The sum of the distances from any point on the ellipse to two fixed points (called foci) is always equal to its major axis.

Property

The ellipse has the property to reflect to a focus any ray produced in the other focus, giving it excellent optical and acoustic properties.

Structure

FOCI:
Are the two fixed points of the ellipse.

HIGHEST PRIORITY:
It is the longest distance between two opposite points.

LOWER SHAFT:
It is the shortest distance between two opposite points.

Special Case

When the plane is perpendicular to the axis of the cone and does not contain the vertex, we obtain a particular ellipse. The circumference.

Special Case

If the plane contains the vertex of the cone we will not have an ellipse but a point.

Eduardo Stefanelli

Engenheiro por profissão, professor por vocação