From the general properties of parabolas (see Parabola.html ) follows that this parabola passes also through the middle K of the segment EF of middles of sides {AC,AB} respectively.

It follows also that the axis of the parabola is parallel to the median AD.

This describes all conics passing through {B,C} and being there tangent to lines {BA, CA} respectively. The letters represent the lines:

x = 0 (line BC),

y = 0 (line CA),

z = 0 (line AB).

The parabola is precisely the conic-member of this family which passes through point K.

In the standard

In fact, consider an arbitrary point D on the basis BC of the triangle and project it parallel to the sides to points C' on AC and B' on AB. The

A proof of this can be found in Artzt_Generation2.html . File Artzt_Generation.html contains a second proof of the same fact using barycentric coordinates.

Another way to generate this parabola can be found in the file ArtztIsosceles.html .

Artzt2.html

Artzt_Generation.html

Artzt_Generation2.html

ArtztIsosceles.html

ArtztCanonical.html

ArtztSteiner.html

BrocardSecond.html

IsoscelesIntersection.html

ParabolaChords.html

ParabolaFromProjections.html

ParabolasFromEqualSegs.html

ParabolaSkew.html

ReflexionsOfLine.html

Symmedian_1.html

ThalesRemarks.html

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