y
12
M
@
Vertex is (0, 0)
Opens up
Focus is (0, 14 )
Directrix is y   14
y  x2
x
y
17
T
Vertex is (3, 1)
Opens right
Focus is ( 3 18 , 1 )
Directrix is x  2 78
x  2( y  1) 2  3
x
y
13
S
$
y  2x  1  2
2
Vertex is (-1, 2)
Opens down
Focus is (-1, 1 78 )
Directrix is y  2 18
x
?
19
P
Vertex is (-2, -1)
Opens up
Focus is (-2,  34 )
Directrix is y  1 14
y  x  2  1
2
#
y
Q
x
2
y
Vertex is (0, 0)
Opens left
Focus is (  14 , 0)
Directrix is x  14
x  y2
x
y
J
%
4
x
x  12   y  32  1
Center is (1, 3)
Radius is 1
y
I
3
x
Center is (0, 0)
Radius is 3
x2  y2  9
y
B
14
x
x  22   y  22  4
Center is (-2, -2)
Radius is 2
y
11
C
>
x
x  22   y  32  4
Center is (2, -3)
Radius is 2
y
15
R
x
x  42  y 2
Center is (-4, 0)
Radius is 5
 25
y
6
A
x  4
2
4
 y  1
Center is (4, -1)
Major axis is parallel to the y-axis
Length of the major axis is 8
Length of the minor axis is 4
2

16
1
x
y
H
x  1
2
16
 y  2
2

4
1
10
Center is (1, 2)
Major axis is parallel to the x-axis
Length of the major axis is 8
Length of the minor axis is 4
x
16
O
!
Center is (0, 0)
Major axis lies on the y-axis
Length of the major axis is 10
Length of the minor axis is 4
x2 y2

1
4 25
K
x  22   y  12
36
4
y
x
5
y
Center is (-2, 1)
Major axis is parallel to the x-axis
Length of the major axis is 12
Length of the minor axis is 4
1
x
y
1
N
x  32   y  12
9
1
Center is (-3, -1)
Major axis is parallel to the x-axis
Length of the major axis is 6
Length of the minor axis is 2
x
G
~
8
Center is (0, 0)
Asymptotes are y  32 x and y   32 x
Vertices are (0, 3) and (0, -3)
y2 x2

1
9
4
D
2
y
x
20
y
Center is (0, 0)
Asymptotes are y  32 x and y   32 x
Vertices are (2, 0) and (-2, 0)
2
x
y

1
4
9
x
y
<
F
18
x
y2 x2

1
16 9
Center is (0, 0)
Asymptotes are y  43 x and y   43 x
Vertices are (0, 4) and (0, -4)
y
&
9
L
x
Center is (0, 0)
Asymptotes are y  52 x and y   52 x
Vertices are (5, 0) and (-5, 0)
x2 y2

1
25 4
y
E
7
x
2
2
x
y

1
9 16
Hyperbola
Center is (0, 0)
Asymptotes are y  43 x and y   43 x
Vertices are (3, 0) and (-3, 0)
y2 x2

1
b2 a2
x2 y2

1
a2 b2
Center is (0, 0)
Center is (0, 0)
Asymptotes are y  ba x and y   ba x
Asymptotes are y  ba x and y   ba x
Vertices are (0, b) and (0, -b)
Vertices are (a, 0) and (-a, 0)
 x  h 2   y  k 2
a2
Ellipse
Circle
b2
1
Center is (h, k)
Center is (0, 0)
If a > b, the major axis is parallel to the x-axis,
the length of the major axis is 2a and the
length of the minor axis is 2b.
If a > b, the major axis is parallel to the x-axis,
the length of the major axis is 2a and the
length of the minor axis is 2b.
If b > a, the major axis is parallel to the y-axis,
the length of the major axis is 2b and the
length of the minor axis is 2a.
If b > a, the major axis is parallel to the y-axis,
the length of the major axis is 2b and the
length of the minor axis is 2a.
x  h 2   y  k 2  r 2
x2  y2  r 2
Center is (h, k)
Center is (0, 0)
Radius is r
Radius is r
y  ax  h   k
x  a y  k   h
Vertex is (h, k)
Vertex is (h, k)
If a > 0, it opens up.
If a < 0, it opens down.
If a > 0, it opens right.
If a < 0, it opens left.
2
Parabola
x2 y2

1
a2 b2
Focus is (h, k 
1
4a
2
)
Directrix is y  k  41a
Focus is ( h  41a , k )
Directrix is x  h  41a
Conic Cards
Deck #8
Conic Cards Deck #8
Parabolas
@
Circles
M
12
T
$
%
Ellipse
Hyperbola
J
4
A
6
17
I
3
H
10
S
13
B
14
O
16
?
P
19
C
11
K
5
#
Q
2
R
15
N
1
>
!
~
G
8
D
20
<
F
18
&
L
9
E
7