QL-P25: 2nd QL-Parabola Focus

QL-P25 is the Focus of the 2^nd QL-Parabola QL-Co3.

For an explanation of the 2^nd QL-Parabola see QL-Co3.

1^st CT-coordinate

a² m n (l – m) (l – n) (l⁵ m⁵ – 3 l⁵ m⁴ n + l⁴ m⁵ n + 2 l⁵ m³ n² – 4 l⁴ m⁴ n² + 2 l³ m⁵ n² + 2 l⁵ m² n³ + 6 l⁴ m³ n³ – 6 l³ m⁴ n³ – 2 l² m⁵ n³ – 3 l⁵ m n⁴ – 4 l⁴ m² n⁴ – 6 l³ m³ n⁴ + 16 l² m⁴ n⁴ – 3 l m⁵ n⁴ + l⁵ n⁵ + l⁴ m n⁵ + 2 l³ m² n⁵ – 2 l² m³ n⁵ – 3 l m⁴ n⁵ + m⁵ n⁵)

-l m n (l – m) (l – n) (m – n) m² n² (4 b² n (l – m) (3 l m – l n – m n))

-l m n (l – m) (l – n) (m – n) m² n² (4 c² m (l – n) (l m – 3 l n + m n))

1^st DT-coordinate

l² (m²-n²) (b² n² (-l²+m²) +c² m² (l²-n²))

Properties

• QL-P25 lies on the line:
  • QL-P8.QL-P17                 (-1 : 3 => QL-P25=Complement of QL-P17 wrt QL-DT)
• QL-P25 lies on the Axis of QL-Co3 which is a line _|_ QL-P1.QL-P7.
• QL-P25 lies on the QL-Medial Circle QL-Ci2.
• QL-P25 lies on the Polar (see [13], Polar) of QL-P9 wrt QL-Co3 and vice versa.
• QL-P25 lies on the Polar of QL-P17 wrt the Polar Circle of the QL-Diagonal Triangle (note Eckart Schmidt).

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