PDST Eccentricity Of Conic Sections

Conic sections have a unifying definition: given a point

, a line

and a real number

, the conic having focus

, directrix

and eccentricity

is the locus of all points

of the plane such that the ratio between their distance from

and their distance from

is equal to

Change the position of the directrix

(by moving points

and

), the position of the focus

and the eccentricity of the conic to observe what kind of curve you get. Verify that the defining condition on

is met for different points

. The conic is

Observe also that when

becomes closer and closer to

the ellipse approximates better and better a circle: when the ellipse is defined by means of its two foci, so its eccentricity

corresponds to the ratio between the focal distance and the major axis,

implies that the two foci are the same point so the ellipse reduces exactly to a circle.

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