Section 10.1 Conic Sections and Quadratic Equations
619
39. (a) y
8x
4p
8
p
2
directrix is x
2,
#
œ Ê œÊœÊ
œ
±
focus is (
), and vertex is (
0); therefore the new
#ß!
!ß
directrix is x
1, the new focus is (3
2), and the
œ±
ß±
new vertex is (1
2)
40. (a) x
4y
4p
4
p
1
directrix is y
1,
#
Ê
œ Ê œ Ê
œ
focus is (
1), and vertex is (
0); therefore the new
!ß±
!ß
directrix is y
4, the new focus is ( 1 2), and the
ß
new vertex is ( 1 3)
±ß
41. (a)
1
center is (
0), vertices are ( 4 0)
x
16
9
y
#
#
²œÊ
!
ß
±
ß
and (
); c
a
b
7
foci are
7 0
%ß!
œ
±
œ
Ê
ß
È
ÈÈ
Š‹
##
and
7
; therefore the new center is (
), the
È
!
%
ß
$
new vertices are (
3) and (8 3), and the new foci are
!ß
ß
47
È
„ß
$
42. (a)
1
center is (
0), vertices are (0 5)
x
92
5
y
#
#
!
ß
ß
and (0
5); c
a
b
16
4
foci are
œ
±
œ
œ Ê
È
È
(
4) and (
4) ; therefore the new center is ( 3
2),
!ß
± ß±
the
new vertices are ( 3 3) and ( 3
7), and the new
±ß±
foci are ( 3 2) and ( 3
6)
43. (a)
1
center is (
0), vertices are ( 4 0)
x
16
9
y
#
#
±œÊ
!
ß
±
ß
and (4 0), and the asymptotes are
or
ßœ
„
x
43
y
y
; c
a
b
25
5
foci are
œ„
œ
² œ
3x
4
È
È
( 5 0) and (5 0) ; therefore the new center is (2 0), the
ß
ß
new vertices are ( 2 0) and (6 0), the new foci
ß
are ( 3 0) and (7 0), and the new asymptotes are
ß
y
3(x
2)
4
±
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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
!
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 Spring '08
 Massman
 Equations, Conic Sections, Conic section

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