Lösungen/Solutions/
B1S2Ue/Ex2

L = Lektion/ Leçon   -- Sprechstunde / heures de consultation
W = Work / Arbeit / Travail
A  =Anhang/  Annexe / Appendice

vecLen[a_] := Sqrt[a . a]

Ueb/Ex 1      W

rM = {5, 7};  R = 3; eM = rM/vecLen[rM]

eM // N

OP1

OP1 = eM (vecLen[rM] - 3)

OP1 // N

OP2

OP2 = eM (vecLen[rM] + 3)

OP2 // N

OP1 . OP2 // Simplify

k[r_] := (r - rM) . (r - rM) - R^2

k[{0, 0}]

OP3

OP3 = {x, y};
solv = 
      Solve[{k[OP3] == 0,  OP3 . OP3 == 65 }, {x, 
          y}]

OP3 = {x, y} /. solv[[2]]

OP3 // N

OP4

OP4 = {x, y} /. solv[[1]]

OP4 // N

OP5, OP6

gP3P4[t_] := OP3 + t ( OP4 - OP3);  gP3P4[t] // N

OP5

solvy = 
      Solve[ gP3P4[t][[1]] == 0, {t}] // Flatten

OP5 = gP3P4[t] /.  solvy // Simplify

N[%]

OP6

solvx = 
      Solve[ gP3P4[t][[2]] == 0, {t}] // Flatten

OP6 = gP3P4[t] /.  solvx // Simplify

OP7, OP8

gP7P8[t_] := OP2 + t ( OP4 - OP3);  gP7P8[t] // N

gOP3[t_] := t OP3;  gOP3[t] // N

gOP4[t_] := t OP4;  gOP4[t] // N

OP8

solvP8 = Solve[gOP3[t1] == gP7P8[t2], {t1, t2}] // Flatten

N[%]

OP8 =  gOP3[t1] /. solvP8[[1]]

N[%]

gP7P8[t2] /. solvP8[[2]] // N

OP7

solvP7 = Solve[gOP4[t1] == gP7P8[t2], {t1, t2}] // Flatten

N[%]

OP7 =  gOP4[t1] /. solvP8[[1]]

N[%]

gP7P8[t2] /. solvP7[[2]] // N

Ueb/Ex 2      W

k[r_] := (r - rM) . (r - rM) - R^2

k[{5, 8}]

Positiv:    a, b:

a = 4;  b = 2;  a b

c, d;   c=d:

Solve[d^2 == 8, {d}] // Flatten

N[%]

e, f:

e = Sqrt[3^2 + 1^2]

N[e]

Solve[e f == 8, {f}] // Flatten

N[%]