Thomas Calculus 13th [Solutions]

Chapter 11 Practice Exercises 869
73.
2 2 2 2 2 2
9x 16y 54x 64 y 1 9 x 6x 16 y 4y 1 9 x 6x 9 16 y 4y
4 144
2 2
2 2
( x 3) ( y 2)
9( x 3) 16( y 2) 144 1, an ellipse; the center is ( 3, 2); a 4 and b 3
16 9
c 16 9 7; the foci are 3 7, 2 ; the vertices are (1, 2) and ( 7, 2)
74.
2 2 2 2 2 2
25x 9y 100x 54y 44 25 x 4x 9 y 6y 44 25 x 4x 4 9 y 6y
9 225
2 2
( x 2) ( y 3)
1, an ellipse; the center is (2, 3); a 5 and b 3 c 25 9 4; the foci are (2, 1)
9 25
and (2, 7); the vertices are (2, 2) and (2, 8)
75.
76.
2 2 2 2 2 2
x y 2x 2y 0 x 2x 1 y 2y 1 2 ( x 1) ( y 1) 2, a circle with center (1,1) and
radius 2
2 2 2 2 2 2
x y 4x 2y 1 x 4x 4 y 2y 1 6 ( x 2) ( y 1) 6, a circle with center ( 2, 1)
and radius 6
77. r 2 e 1 parabola with vertex at (1, 0)
1 cos
78. r 8 4 1
2 cos r e 1
1
cos 2
ellipse;
2
ke 4 1 k 4 k 8; k a ea 8 a 1 a
2 e
2
a 16 ea 1 16 8
3 2 3 3 ; therefore the center is
8
3 , ; vertices are (8, ) and 8
3 , 0
1
2
79. r 6 e 2 hyperbola; ke 6 2k
6
1 2cos
k 3 vertices are (2, ) and (6, )
80.
r 12 r 4 e 1 ; ke 4
3 sin 1 sin 3
1 k 4 k 12;
3
1
3
2
2
a 1 e )4 a 1 1 4
3
a 9 ea 1 9 3
2 3 2 2 ; therefore the center is
3 , 3 ; vertices are 3, and 6, 3
2 2
2
2
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