QL-P23: Center of the Inscribed Midline Hyperbola

 
QL-P23 is the center of the Inscribed Midline Hyperbola. This is the conic touching the defining lines of the Reference Quadrilateral and with the Newton Line as asymptote. See Paragraph QL-Co2.
 
 
QL-P23-CenterMidlineHyperbola-01
 
Coordinates: 
1st CT-coordinate:
            l (m - n) ((l m + l n + m n)2 - 4 m n (l2 + m n))
 
1st DT-coordinate:
            m2 n2 (m2-n2)
 
 
 
Properties:
  • QL-P23 lies on QL-L1, the Newton Line.
  • QL-P23 lies on QL-L9, the M3D Line.
  • QL-P23 is the common point of the Newton Lines of Quadrilaterals (L1,L2,L3,QL-L1), (L2,L3,L4,QL-L1), (L3,L4,L1,QL-L1), (L4,L1,L2,QL-L1). See Ref-50, Dao Thanh Oai, ADGEOM-messages #3110, #3111.

 

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