2 inscribed parabola
- Hello everyone,
I only know of 2 cataloged inscribed parabolas: the Kiepert and Yff
parabolas with perspectors :1/(cc-aa): and : 1/(c-a) :.
The affine methods I have been creating show that each inparabola can
be associated with a line through G. The Kiepert parabola is
associated with GK and the original Yff parabola (there are actually
four of them) with GIo, where Io is the original incenter.
(Details of this can be found on my web pages, linked below. Check
out the section on lines though G in the document on conic types. )
The Jerabek hyperbola leads to two interesting inparabolae.
Note: the "switched" conic has center and perspector interchanged.
The line from G through J, the Jerabek center leads to the inparabola
perspector: intersection of the Jerabek hyperbola and the Steiner
Focus: the T, the Tarry point.
Axis: through T parallel to HD, where D = tH, the isotomic of H.
Directrix: H U, where U is the 4th intersection of the switched
Jerabek hyperbola with the Steiner ellipse.
The other comes from the line between G and the Jerabek perspector.
perspector: U, the intersection of the switched Jerabek hyperbola
and the Steiner ellipse
Focus: the "pro" of this point
Axis: through focus parallel to ~J, where J is the Jerabek center.
The arml website is now officially on line. Find it here.
The Secrets of Georgia ARML 1
Find it here.
The Secrets of Georgia ARML 3 website, is at
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