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SOLUTIONS DES EXERCICES

54

4.52. 70.75°

4.70. b. 10x – 11y + 2z – 34 = 0

4.53. α = 40.53°, β = 99.76°, γ = 39.71°

4.71. p’ : 12x + 4y + 3z – 209 = 0
p’’ : 12x + 4y + 3z + 129= 0

4.54. 52.67°

4.72. b. Ω (–1 ; 2; 3), r = 8

4.55. 36.58°
4.73. I(1; 2; –2) et J(3; 0; –1)
4.56. a. x2 + y2 = 9
b. x2 + y2 – 12x + 16y = 0

4.74. c. g :

c. x2 + y2 – 2x – 8y + 9 = 0
2

2

{

x=−2
y=2
z=3

d. x + y – 4x – 8y + 10 = 0

4.76. b. 2x + 6y – 3z – 63 = 0

4.57. a. Ω(–3 ; 0), r = 5
b. Ω(–3 ; 4), r = 3
c. Ce n’est pas un cercle
d. Ω(2.25 ; –1), r = 3.17

4.58. (x–4)2 + (y–2)2 = 25
4.59. a. A(0 ; –3)

B

 
11 7
;
5 5

b. T(3 ; 1)



3 4
B − ;−
5 5

4.60. A(–1 ; –1)



4.61. a. A(0.71 ; –0.12)
b. B(–3.5 ; 1.25)

4.62. a. 3x – 4y = –43
b. 2x + y = –19
c. x – 2y = –11

2x + y = 1
2x + y = 8

4.63. a. x2 + y2 – 2x = 0
b. (x–2)2 + (y–1.5)2 = 4

4.64. a. x2 + y2 + z2 = 14
b. (x–1)2 + (y+2)2 + (z–4)2 = 45

4.65. (x–3)2 + (y–2)2 + (z+1)2 = 56
4.66. a. oui

Ω (–3; 5; 2)

r=4

b. non
c. oui





1
1
; – 2; –
2
2



r= 4  3

4.67. (x–4)2 + (y+1)2 + (z–3)2 = 45
8
4.69. r= 3

Cahier Géométrie

Didier Müller - LCP - 2012