Chapter 6: Analytic Geometry
6.1:
Circles and P
ar
abolas
1.
The equation is that of a circle with center (3, 3) and radius 0.
That is, the graph is the point (3, 3).
2.
The equation is that of a circle with center (3, 3) and radius
.
No such graph exists.
3.
E.
Since
is equivalent to
, this is a parabola that opens to the right
.
4.
C.
Since
is equivalent to
, this is a parabola that opens upward
.
5.
H.
Since
is equivalent to
, this is a parabola that opens downward
.
6.
B.
Since
is equivalent to
, this is a parabola that opens to the left
.
7.
F.
This is the equation of a circle centered at the origin with radius
.
8.
A.
This is the equation of a circle centered at the point
with radius
.
9.
D.
This is the equation of a circle centered at the point
with radius
.
10. G.
This is the equation of a circle centered at the origin with radius
.
No such graph exists.
11. Here
.
The equation is
.
12. Here
.
The equation is
.
13. A circle that is centered at the origin with
has equation
.
14. A circle that is centered at the origin with
has equation
.
15. Here
.
The equation is
.
16. Here
.
The equation is
.
17. The radius is the distance between
:
Here
.
The equation is
.
18. The radius is the distance between
:
Here
.
The equation is
.
19. If the center is
, the circle must touch the
x
-axis at the point
.
The radius is 2.
Here
.
The equation is
.
20. If the center is
, the circle must touch the
y
-axis at the point
.
The radius is 5.
Here
.
The equation is
.
21. The center is the midpoint on the diameter between
:
22. The radius is the distance from the center
to an endpoint
:
23. Here
.
The equation is
.
1
x
2
2
2
2
1
1
y
1
3
2
2
5
45
h
5
2,
k
5]
3 and
r
2
5
1
1
45
2
2
5
45
r
5
2
1
2
2
1
]
1
22
2
1
1
]
3
2
3
2
2
5
1
9
1
36
5
1
45
5
3
1
5
1
]
1, 3
2
1
2,
]
3
2
M
5
a
]
1
1
5
2
,
3
1
1
]
9
2
2
b
5
1
2,
]
3
2
1
]
1, 3
2
and
1
5,
]
9
2
1
x
2
5
2
2
1
1
y
1
1
2
2
5
25
h
5
5,
k
1 and
r
2
5
5
2
5
25
1
0,
]
1
2
1
5,
]
1
2
1
x
1
3
2
2
1
1
y
1
2
2
2
5
4
h
3,
k
2 and
r
2
5
2
2
5
4
1
]
3, 0
2
1
]
3,
]
2
2
1
x
2
2
2
2
1
1
y
1
7
2
2
5
25
h
5
2,
k
7 and
r
2
5
5
2
5
25
r
5
2
1
2
2
1
]
2
2
1
1
]
7
2
1
]
4
2
5
1
16
1
9
5
5
1
2,
]
7
2
and
1
]
2,
]
4
2
1
x
1
1
2
2
1
1
y
2
2
2
2
5
25
h
1,
k
5
2 and
r
2
5
5
2
5
25
r
5
2
1
2
2
1
]
1
2
1
1
6
2
2
2
2
5
1
9
1
16
5
5
1
]
1, 2
2
and
1
2, 6
2
a
x
1
1
2
b
2
1
a
y
1
1
4
b
2
5
144
25
h
1
2
,
k
1
4
and
r
2
5
a
12
5
b
2
5
144
25
a
x
2
2
3
b
2
1
a
y
1
4
5
b
2
5
9
49
h
5
2
3
,
k
4
5
and
r
2
5
a
3
7
b
2
5
9
49
x
2
1
y
2
5
25
r
2
5
5
2
5
25
x
2
1
y
2
5
1
r
2
5
1
2
5
1
1
x
1
2
2
2
1
1
y
2
5
2
2
5
16
h
2,
k
5
5 and
r
2
5
4
2
5
16
1
x
2
1
2
2
1
1
y
2
4
2
2
5
9
h
5
1,
k
5
4 and
r
2
5
3
2
5
9
1
]
4
1
25
5
5
1
]
3, 4
2
1
25
5
5
1
3,
]
4
2
1
5
1
c
6
0
2
y
2
5
4
a
]
3
4
b
x
y
2
3
x
1
c
6
0
2
x
2
5
4
a
]
3
4
b
y
x
2
3
y
1
c
7
0
2
x
2
5
4
a
1
8
b
y
y
5
2
x
2
1
c
7
0
2
y
2
5
4
a
1
8
b
x
x
5
2
y
2
1
]
1