ellipse a=8/5, b=1; caustic lambda=64/169; a''^2=9216/4225, b''^2=105/169
foci at (+-c,0), c = None

##### DELIBERATELY WRONG INPUTS (every one must be rejected) #####
(1) lambda = 64/169 + 1/10000, orbit built by reflection from (a,0) with the lambda=64/169 tangent direction:
    sides tangent to the wrong caustic: [False, False, False, False, False, False]  closes after 6: True  -> rejected: True
(2) true caustic, initial direction perturbed by 1/1000:
    sides tangent: [False, False, False, False, False, False]  closes after 6: False  -> rejected: True
(3) does the lambda=64/169 orbit close after 3 bounces (it must not): False
(4) vertex P2 moved by 1e-6: all on ellipse: False  side P1P2 tangent: False  -> rejected: True
(5) A' of orbit I equals 96*sqrt(105)/175: True ; equals 97*sqrt(105)/175 (wrong): False
