6eeffcef-67ca-4d61-a6e5-46db90ac3f34 10 4 5 fraction

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Solving Doublet ...=>

... forms the complex genaratrix of: circle/ellipse, parabola.

x y Doublet y R 2^- x 2^+ y 2^+ (* x 2^y 2^+ / :

y F x y Doublet 0 ≡ x solve maple :

y F R y - (R y + (* sqrt R y - (R y + (* sqrt - 21 mat

R 1 :

x F 1 el Re x F 2 el Re x F 1 el Im x F 2 el Im 4 1 sys

Maxima X_Y does NOT plot conditional parametric

x R F R y - (R y + (* sqrt R y - (R y + (* sqrt - 21 mat :

α 0.5 :

Circle/Ellipse(s) and parabola(s)

R α 21 mat Distance Focus 21 mat ≡

x R Incl R - x ≤ (x R ≤ (& α R x - (R x + (* sqrt * α R x - (R x + (* sqrt - (* 21 mat inclusive if :

x R Excl_1 x - R ≤ (R x ≤ (& exclusive α R x - (R x + (* sqrt * α R x - (R x + (* sqrt - (* 21 mat if :

R 0.5 :

Circle/Ellipse [R/α]

x 1 Incl 1 el Re x 0.5 Incl 2 el Re 2 1 sys

x R Excl_2 x - R ≤ (R x ≤ (& R x - (R x + (* sqrt R x - (R x + (* sqrt - 21 mat exclusive if :

Parabolas [ R/α ]

x R Excl_1 1 el Im x R Excl_1 2 el Im x R Excl_2 1 el Im x R Excl_2 2 el Im 4 1 sys

x 0.5 Excl_1 1 el Im x 0.5 Excl_1 2 el Im 21 sys Left parabola ≡

x 0.5 Excl_2 1 el Im x 0.5 Excl_2 2 el Im 21 sys right parabola ≡

Plotting both parabolas, they track on 0_axis