Thomas Calculus 13th [Solutions]

Section 12.1 Three-Dimensional Coordinate Systems 879
39. (a)
2 2 2
( x 1) ( y 1) ( z 1) 1
(b)
2 2 2
( x 1) ( y 1) ( z 1) 1
40.
2 2 2
1 x y z 4
41.
2 2 2
P1 P2 (3 1) (3 1) (0 1) 9 3
42.
2 2 2
P1 P2 (2 1) (5 1) (0 5) 50 5 2
43.
2 2 2
P1 P2 (4 1) ( 2 4) (7 5) 49 7
44.
2 2 2
P1 P2 (2 3) (3 4) (4 5) 3
45.
2 2 2
P1 P2 (2 0) ( 2 0) ( 2 0) 3 4 2 3
46.
2 2 2
P1 P2 (0 5) (0 3) (0 2) 38
47. center ( 2, 0, 2), radius 2 2 48. center 1,
1
, 3 , radius 5
2
49. center 2, 2, 2 , radius 2 50. center 0,
1
,
1
, radius 4 3 3
3
51.
2 2 2
( x 1) ( y 2) ( z 3) 14
52.
2 2 2
x ( y 1) ( z 5) 4
53.
2 1
2
2
2
16
2 3 81
( x 1) y z 54.
2 2 2
x ( y 7) z 49
55.
2 2 2 2 2 2 2 2 2
x y z 4x 4z 0 x 4x 4 y z 4z 4 4 4 ( x 2) ( y 0) ( z 2) 8
2
the center is at ( 2, 0, 2) and the radius is 8
56.
2 2 2 2 2 2 2 2 2 2
x y z 6y 8z 0 x y 6y 9 z 8z 16 9 16 ( x 0) ( y 3) ( z 4) 5
the center is at (0, 3, 4) and the radius is 5
57.
2 2 2 2 2 2
2x 2y 2z x y z 9 x 1 x y 1 y z 1 z 9
2 2 2 2
2 1 1 2 1 1 2 1 1 9 3 1
2
1
2
1
2 5 3
x x y y z z x y z
2 16 2 16 2 16 2 16 4 4 4 4
the center is at 1 , 1 , 1 and the radius is 5 3
4 4 4
4
2
Copyright
2014 Pearson Education, Inc.