f5cc83a2-ac85-4ec3-8765-dfb4477169ab 7 15 12 decimal

&[DATE] &[TIME] - &[FILENAME]

Solving the ellipse/line intersection [Smath Designers]

============================================== solving 1rst intersection

determined condition
determined condition f 2 x 2^* 3 y 2^* + 59 - 0 ≡ x - 4 y * + 8 - 0 ≡ 21 mat :

Guess roughly x.0 x 1.25 ≡ y 0.75 ≡ 21 mat :

Accuracy TOL 1015 -^:

most robust for this example sol_1 f x.0 TOL LevenbergMarquardt :

sol_1 4321 mat

x y E 2 x 2^* 3 y 2^* + 59 - :

u λine u 8 + 4 / :

x y axes x y / - :

============================================== solving 2nd intersection

x y Clear 1

determined condition
determined condition Φ 2 x 2^* 3 y 2^* + 59 - 0 ≡ x - 4 y * + 8 - 0 ≡ 21 mat :

Guess wisely y.0 x 7 - ≡ y 0.75 ≡ 21 mat :

Accuracy TOL 1015 -^:

most robust for this example sol_2 Φ y.0 TOL LevenbergMarquardt :

sol_2 5.371429 - 0.657143 21 mat

E u λine sol_1 1 el sol_1 2 el 1 2 mat axes sol_2 1 el sol_2 2 el 1 2 mat 5 1 sys

E u λine sol_1 1 el sol_1 2 el 12 mat axes sol_2 1 el sol_2 2 el 12 mat 51 sys