Geometric Construction for Hyperbola and Ellipse

This applet gives a geometric construction for two conics - hyperbola and ellipse, based on the definitions below. We start with two fixed points

and

(the vertices of the conics) and two points

and

(the foci of the conics), on a variable distance

from the vertices. A hyperbola is the locus of all points

in the plane such that the absolute value of the difference of the distances from

to two fixed points

and

(the foci) is a constant equal to the distance between the vertices:

An ellipse is the locus of all points

in the plane such that the sum of the distances to two fixed points

and

(the two foci) is a constant, equal to the distance between the vertices:

In this construction the locus is based on a point

moving along a circle with a center one of the foci and radius equal to the distance between the vertices.

Press the play button to animate point .
Drag the slider to change the distance from the foci to the vertices.
Consider the two cases -- the foci outside of the vertices and the foci between the vertices.
You can follow the construction steps with the controls at the bottom of the applet.

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