tangent  At each point on a conic, there is a unique tangent defined as the limiting position of a chord. The macro constructs the tangent if the point lies on the conic  otherwise it returns a line which is not a tangent to the conic. 
tangent pair 
If a point does not lie on a conic, then there are two possibilities. Either there are no tangents to the conic through the point
(when we say the point lies inside the conic),
or there are exactly two tangents (and the point lies outside the conic). The macro draws the pair of tangents in the latter case, and nothing in the former. 
four tangents  Given two conics, there can be up to four lines which touch both. The macro produces all of these common tangents. 
envelope  A conic is usually defined as a set of points (a pointconic),
but it can equally well be defined as the envelope of the set of tangents
(a lineconic). The macro shows some of the tangents for a pointconic, confirming that the envelope is the original pointconic.

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