QA-L2: QA-P2-P4-P6 Line

The QA-L2-line is the line through QA-P2 (Euler-Poncelet Point) and QA-P4 (Isogonal Center). QA-P6 (Parabola Axes Crosspoint) also lies on this line and is their Midpoint. The expression of the line is not a simple one.

1st CT-coefficient:

b² p r² (2 SA p – 2 SB q) ((b² – a²) p q + b² p r – a² q r) (b² p r + (b² – a²) p q + (b² – c²) q r – 2 SB q²)

– c² p q² (2 SA p – 2 SC r) ((c² – a²) p r + c² p q – a² q r) (c² p q + (c² – a²) p r + (c² – b²) q r – 2 SC r²)

1st DT-coefficient:

(c² q² – b² r²) (-a² p² (c⁴ q⁴+b⁴ r⁴)+(b⁴ p⁴+a⁴ q⁴) r² SB+q² (c⁴ p⁴+a⁴ r⁴) SC+2 a² p² q² r² (SA²-SB SC))

Properties

• QA-L2 = QA-P2.QA-P4 // QA-P1.QA-P32 // QA-P7.QA-P8 // QA-P12.QA-P24 // QA-P11.QA-P38
• QA-L2 and the 5^th Point tangent at QA-P2 are orthogonal. See QA-Tf9.
• QA-L2 and the asymptote of QA-Cu7 (QA-Quasi Isogonal Cubic) are perpendicular. See QA-Cu7 and QA-4.
• The QA-Möbius Conjugate (QA-Tf4) of QA-P41 is a point on QA-L2.

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