Algebra 2
Unit 3 WS 3-1: Identifying All Conies
Name:
Introduction to Conic Sections
Each conic section is formed by passing a
i I
Explain how each is formed and sketch a picture for each:
Circle:
Parabola:
Ellipse:
n_ojh
S v
Hyperbola:
par*,
through a
Classify each of the following conies as a parabola (P), circle (C), ellipse (E), hyperbola (H)
GENE/ARAL FORM EQUATION
1) x2 + y2 - 6x + 4y + 9 = 0
2) x2 + 4y2 - 6x + 16y + 21 = 0
3) 4x2 - y2 - 4x - 3 = 0
4) y2 - 6y - 4x + 21 = 0
5) y 2 - 4x2 + 4x - 2y - 4 = 0
6) x2 + y2 - 4x + 6y - 3 = 0
7) x2 - 4x - 8y + 2 = 0
8) 4x2 -H y2 - 8x * 3 = 0
9) 4x2 + 3y2 + 8x - 24y H- 51 = 0
10) 4y2 - 2x2 - 4y + 8x - 15 = 0
11) 25x2 - lOx - 200y - 119 = 0
12) 4y2 + 4x2 - 24x + 35 = 0
13) 4x2 -H 16y2 - 4x - 32y + 1 = 0
14) 2y2 + 2x + 2y + 1 = 0
15) lOOx2 * lOOy2 - lOOx + 400y + 409 = 0
16) 4x 2 - y 2 + 4x + 2y -1 = 0
CONIC SECTION
C
£
A
P
H
C
P
£
£
H
P
c
e
p
c
ri
Algebra 2
Unit 3 WS 3-2: Circles
Name:
Find the center and the radius of each circle whose equation is given. Then draw the graph.
1.
CP:
O-4) 2 +O + l ) 2 = 2 0
Radius =
2.
3jc 2 +3/=27
zo
Radius =
3
0
r
A
-
n 3 _n
/
*-v
^ -I•i
/
|^
.
V
p
"v
n
s.
/3
4
>(
y
i
i i• 1
/
X
A
r.
_
8n
1
Complete the square on the following equations to find the standard format of a circle.
3. x 2 +/-6x-12^ + 36 = 0
4. 4x2+4y2
Algebra 2
Units WS 3-3: Parabolas
Name:
Find the following information and draw the graph. Include ALL pieces of information!!
2.
O"
r\
r
s,
1
n - j .-\
I
/
4
d
>^>
j
s*
1
n
I
•
I
1
\s
\
\
X.
^
1V
-10.-= 3.
II
4
n
,n
Distance Calculation:
Distance Calculation:
- 2_
Vertex :
Vertex:
Focus:
Focus:
Axis of Sym:
Axis of Sym:
Directrix:
Directrix:
Dir of Opening:
Dir of Opening:
^u O
0-J.D
3.
4.
x = -— ( y + l ) 2 - 4
12
x = — (y-2)
16
/f
~&
-1QT-
\
-10- L
M
Distance Calculation:
Distance Calculation:
J- ,
Vertex :
Vertex:
Focus:
Focus:
AxisofSym:
V ~ - \:
Dir of Opening:
Axis
isofSym:
M -" )
A
Directrix:
Dir of Opening:
i ~
Complete the square on the following equations to find the standard format of a parabola.
5.
6.
20x = -5y2 -10^ + 15