QA-Cu4: QA-DT-P19 Cubic


QA-Cu4 is the locus of the Double Points created by the QA-Line Involution (QA-Tf1) of all lines through QA-P19.
It is a pivotal isocubic of the QA-Diagonal Triangle, invariant wrt the Involutary Conjugate with pivot QA-P19.
QA-Cu4 is a pK(QA-P16,QA-P19) cubic wrt the QA-Diagonal Triangle in the terminology of Bernard Gibert (see Ref-17b). (note Eckart Schmidt)
 
QA-Cu4-QA-DT-P5-P10-Cubic-00
 
Equations: 
Equation CT-notation:
   r2 (p+q) (p+q+2r) (p2 + q2) (q x - p y) x y
+ q2 (p+r) (p+2q+r) (p2 + r2) (p z - r x) x z
+ p2 (q+r) (2p+q+r) (q2 + r2) (r y - q z) y z = 0
Equation DT-notation:
(-p2+q2+r2)(r2 y2-q2 z2)x +(p2-q2+r2)(-r2 x2+p2 z2)y + (p2+q2-r2) (q2 x2-p2 y2) z = 0

Properties: