Thomas Calculus 13th [Solutions]

842 Chapter 11 Parametric Equations and Polar Coordinates
33.
2 2
2 2 y x
2 2
2 8
2 8 10; asymptotes are y
x
2
8y 2x 16 1 c a b
34.
2 2
2
x y
2 2
36 64
64x 36y 2304 1 c a b
36 64 10; asymptotes are y
4
3
2
35. Foci: 0, 2 , Asymptotes: y x c 2 and
2 2
b 1 y x 1
a
b
2 2 2 2 2
1 a b c a b 2a 2 2a a 1
36. Foci: ( 2, 0), Asymptotes: y 1 x c 2 and
2 2
4 2 2
4 a a 3 a 3 b 1 x y 1
3 3
3
2 2
b 1
2 2 2 2
b a c a b a a 4 a
a 3 3
3 3
37. Vertices: ( 3, 0), Asymptotes: y 4 x a 3 and
3
b
a
2
4 4
y
b (3) 4 x 1
3 3 9 16
2
38. Vertices: (0, 2), Asymptotes: y 1 x a 2 and
2
a
b
2 2
1
y
b 2(2) 4 x 1
2 4 16
39. (a)
2
y 8x 4 p 8 p 2 directrix is
x 2, focus is (2, 0), and vertex is (0, 0);
therefore the new directrix is x 1, the new
focus is (3, 2), and the new vertex is (1, 2)
(b)
40. (a)
2
x 4y 4 p 4 p 1 directrix is
y 1, focus is (0, 1) and vertex is (0, 0);
therefore the new directrix is y 4, the new
focus is ( 1, 2), and the new vertex is ( 1, 3)
(b)
41. (a)
2
x 2 y
1
16 9
center is (0, 0), vertices are
2 2
( 4, 0) and (4, 0); c a b 7 foci
are 7, 0 and 7, 0 ; therefore the new
center is (4, 3), the new vertices are (0, 3) and
(8, 3), and the new foci are 4 7, 3
(b)
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