620
Chapter 10 Conic Sections and Polar Coordinates
44. (a)
1
center is (
0), vertices are (0
2)
y
45
x
#
#
±œÊ
!
ß
ß
±
and (0 2), and the asymptotes are
or
ßœ
„
y
2
x
5
È
y
; c
a
b
9
3
foci are
œ„
œ
² œ
œ Ê
2x
5
È
È
È
##
(0 3) and (0
3) ; therefore the new center is (0
2),
ßß
±
ß
±
the new vertices are (0
4) and (0 0), the new foci
ß±
ß
are (0 1) and (0
5), and the new asymptotes are
±
y2
²œ„
2x
5
È
45. y
4x
4p
4
p
1
focus is (
0), directrix is x
1, and vertex is (0 0); therefore the new
#
œ Ê œÊœÊ
"
ß
œ
±
ß
vertex is ( 2
3), the new focus is ( 1
3), and the new directrix is x
3; the new equation is
±ß±
œ±
(y
3)
4(x
2)
²œ²
#
46. y
12x
4p
12
p
3
focus is ( 3 0), directrix is x
3, and vertex is (0 0); therefore the new
#
Ê
œ
Ê œ Ê
± ß
œ
ß
vertex is (4 3), the new focus is (1 3), and the new directrix is x
7; the new equation is (y
3)
12(x
4)
œ
±
œ
±
±
#
47. x
8y
4p
8
p
2
focus is (0 2), directrix is y
2, and vertex is (0 0); therefore the new
#
ß
œ
±
ß
vertex is (1
7), the new focus is (1
5), and the new directrix is y
9; the new equation is
(x
1)
8(y
7)
±œ²
#
48. x
6y
4p
6
p
focus is
, directrix is y
, and vertex is (0 0); therefore the new
#
#
œ
Ê
œ
Ê
œ
Ê
!ß
œ ±
ß
33
3
ˆ‰
vertex is ( 3
2), the new focus is
3
, and the new directrix is y
; the new equation is
"
7
(x
3)
6(y
2)
#
49.
1
center is (
0), vertices are (0 3) and (
3); c
a
b
9
6
3
foci are
3
x
69
y
#
#
²
œ
Ê
!ß
ß
!ß±
œ
±
œ
± œ
Ê
!ß
È
ÈÈ
È
Š‹
and
3 ; therefore the new center is (
1), the new vertices are ( 2 2) and (
4), and the new foci
È
±#ß±
± ß
are
1
3 ; the new equation is
1
È
±#ß± „
²
œ
(x
2)
(y
1)
±±
50.
y
1
center is (
0), vertices are
2
and
2
; c
a
b
2
1
1
foci are
x
2
#
²œÊ
!
ß
ß
!