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The Kiepert parabola is the envelope of the perspectrix of the perspective triangles 
and 
obtained when similarly oriented similar isosceles triangles 
, 
, and 
are constructed on the sides
of a triangle 
and their common vertex
angle is varied. It has trilinear conic function
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This parabola was first studied by Artzt (1884; Eddy and Fritsch 1994).
The Euler line of a triangle is the conic section directrix of the Kiepert
parabola. In fact, the directrices of all
parabolas inscribed in
a triangle pass through the orthocenter.
The Brianchon point for the Kiepert parabola is
the Steiner point 
of the reference triangle,
and the triangle 
formed by the points of contact is called the
Steiner triangle.
The Kiepert parabola is tangent to the sides of the triangle (or their extensions), the line at infinity, and the Lemoine axis. The focus of the parabola has triangle center function
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and is Kimberling center 
. For a scalene triangle,
the vertex of the Kiepert parabola is Kimberling
center 
(Kimberling).
The Kiepert parabola passes through Kimberling centers 
for 
(the isogonal conjugate
of the focus of the Kiepert parabola 
), 669 (the crossdifference
of 
and 
),
1649, and 2528 (Weisstein, Oct. 16 and Dec. 13, 2004).
The polar triangle of the Kiepert parabola is the Steiner triangle.
The Kiepert parabola focus and Parry point are the two intersections of a triangle's circumcircle with its Parry circle.
is also the Feuerbach
point of the tangential triangle of 
.
