### 5-22-17 Conic Sections Review KEY

```Name_~~4·
Date,
Algebra II Pre AP
Conics Review Worksheet
~
_
Period __
Identify the conic and write each of the following in standard form.
c
c
(1t-
2..) ~ -I- ~ ~.::. Olo
S-r- = I~
(1[-1) ~ f. (,+
3):a.
(J{+
E
I
"J!2..
-'1
G
(!1-z.)
+-
1. X2 + y2 - 4x -16
2-
::
I
==
I
4-
+ ( 'J ~L)
2.
2. X2 + y2 - 2x
-/j (y -3) ~
~:-i (~_
¥)
C!::J -I )
, =I
-4
'K--:
fJ
f
_
(1t+3);J..
/I
I
(jc-LJ:a.
q-
4.
X2+9y2 -36y+27
6. X2- 8x
=0
=0
=0
+ 2y + 16 = 0
7. X2_4y2 +Sy-S
~
8. X2_9y2 +6x
-
(~~t)
.,-
=0
-
=/
2
9. 9x +4y2 -36x+Sy+4
I
=0
10. 16x2 _9y2 -32x-54y-209
IfIJ
9
=0
2-
(XJ-L):l._ (fJ 1-3)2.;:
f/
4X2 + y2 +24x-4y+36
!Jl..._1
9
e-
3.
2.
']C2..
tI
+ 10y + 10 = 0
5. y2 -4x-6y+9
1-
=0
=0
Write each of the following in standard form then find all appropriate information.
11.
4X2 +9/ +Sx-36y+4
center
(-I,
=0
a..)
-'-If z. J (2., 2..)
endpts of minor axis
(-(It))
( - I:!: If5=- I
endpts of latus rectum
(-
2-, -
foci
5", -if-)
(~o)
(
!»J
.!:.J
-8 J
(S-:t..:l
(S-, - L/ 1: ;J.. VZ
equations of asymptotes
't
-z:-
-4)
)
-? l.j ~
eccentricity
VI()(-s)
z!.
""""i:""
y2+x+2y-8=O
vertex
( ;!cf, ! J
=
(Cj l -I)
focus ---=-+--
\{{OJ
v:ll
~
:J
14.
i=)
=0
endpts of conjugate axis
2-)
I
x2+/+4x+9y-1=O
center
(-I, L/)
(-/ ~ Vs
3
(
vertices
(-I :f. v_
'~J
'~)
~~4___
.e:«:
V~
eccentricity
2X2 - y2 -20x-Sy+50
center
endpts of major axis (
foci
13.
12.
equation of directrix
_-=-~,,---':.
__
equation of axis of symmetry
endpts of latus rectum
si.
c..(
fj:. -I
-3 )
(g
1./, 2:
(H
tt I
-J.)
Z.
Using the following
information,
write an equation
( 1{.... "I"1)~ of-( 9-7) ~-::: i:J.S
~ 15.
(X" 7 J.) 1.. +- 'J ~ :=
( ~-'I) LI- (fj-4
t{
8 L/ ()
(1(-3)
.l:!I
_---"y"--
J
18. Circle with center at
.,lS-__________
19. Ellipse foci
(y-3J 20
+ -;;-::I
(1.j-4) 'z,
(~-"iI
--;-c -
J
at
(6, 22)
= 4 and tangent to both axes
(6, 9) and tangent to the circle X2 + y2 + 4x - 6y -12 = 0
(3,
(3,
2) and
11) and sum offocal radii is 16
20. Ellipse tangent to the x and y axis and the line x
20
()
1,3
and
(
9,3
= 10
with foci at
)
l! - :. I
21. Vertical hyperbola with asymptotes y
(jj-~)").
(~_.s-)l.
I,.
I
__________
(x.,...l.)
= 3x + 4
"2-
ID_T-'---- __
('t-s-)~
(1, 2) and (6, 12)
Endpointsofdiameter
17. Circle with center in the first quadrant on the line x
ZS'"
of- (y- u.2.
/ (/
2.
Show all work.
16. Circle with center on the x axis and tangent to the line y
)l..: ,(.,
(JC-G,)l.of-(~-ttl~
in standard form.
= 2x + 3
and y
= -2x + 5
and the
difference of the focal radii is 8
== I
22. Hyperbola vertices at (5,
7) and (5,
9)
and length of the conjugate
axis is 8
{9-2.)'"
l..
_-::_/~~~___ •._'1_-_.::._I_
23. Hyperbola with center (-2, 2), a focus at (2, 2) and and length of the
conjugate axis is 4
u= ",-..L ('K-{)~+.:ff
J-
2. 24. parabola with directrix y
2..
1C tz (':1 -
.3 )
1. -
2..
25. parabola with directrix
x
= 3 and a focus
= _2.
at (1, 2)
and a vertex at (-2, 3)
4
26. parabola where the directrix is the x-axis and the focus is (5, 1)
,'(
1t
= 2:i q -I.{)
-a.
- ~ 27.
parabola with the vertex at the center of the hyperbola
9x2 - 4 y2 + 90x + 8y + 185 = 0 and the focus at the center of the circle
X2 + y2 - 4x - 2y - 20 = 0
28. circle whose diameter is the line segment joining the vertex and the focus of the
parabola
X2 -12y
=0
;;- .?"-
Graph each of the following and indicate the domain and range.
Y = 2.J1- X2
29.
r ---P,"' ~
T
..
I-
t
1L =/
a, -l-
(':1-1-)
&
-rr-r-r-r-
I~
-1-, Tf'T']
r
!
I
I
!
I
I
I
I
i
I
!
!
4-
!....
-
-13 -
-
'"
I
I
I
!
!
,
T 8
!
I
I
·8
I
-R
t
!,
i
I
-~25+4y-
~
S
!
14
I
1
j
!
r
-
I
I••
:'
-.S - - -5 -It - -12 -it
1
I
II
I
I
j
1
8
r
I
,
I
I
"
,v
vV'·
y>2-~36-4(X-1)2
(!:J-J...)
1-
..:~'V
!~
34.
jcl2..
CF .f-~_I
v
,
I
,
1
,
j
!
I
I
y2
+- (lj-2..)~= ~9
L
I
-r
r
I
r
7
'L:.
ec
-4(x-I)
4(Y-I)~ +(lj-""L)'=
(1c-O'Z. + (&-2.)
-9
c;-r-r
,
I
-
i I
I
!
I
j
f
l
II'
!
I
I
I
,
j
1 I
rI
- -
! I
I
I
!
',1
1/
i
1
I
A•..•
v
1/
~'\
If
1/,
-B -Q
3 ,1,
-,
J
!
!
. '0\
f
!
i
I
I
I
I
1
I
I
!
!
(
I
,
I
I
I
1
I
I
I
i I
i
I
i 1
I
8-
!
I
.
I.
I
i
I I
r--P1+
f'..j
, 1
.
i
1
-~
1
I
I
!
I
I
i
I....-r
~
I
I~
1
,
.v c/ - Dr"-
.
T 3
-B-
I
!
j
I
I
,
j
!
T
I
I
!
~
3'
2
=t
.. r-t-r+-v-t-
'IL
1/1
Y
I
I••• 1/
I)
t>
1...-
I
i
4-
I
!
I
I
r
f
i
.1- f.--6
~
rv
I
,
1
I,
~
8-
I
1
I~
,
I
r-n-&
r
r
r
·5
I
f-- +l-
r
8
I
J
l,..;
-l? -"
!
I
I I
1C.2.
. .s
1
I
!
I
I
I
!
I
j
32. X:::;
4
I
r
!
I
!
,
r
!
I
I
I'
~
IF
-
'J ;-(k: _3)1.+
9
'2..:::.
I-~
If
j I
i I
I I
,
x>~1-y+3
("-3):
~~U
2-
'K2-
31.
-
~k..t
SIu.J..-
X=~9-(Y-2)2
30.
~AJ
f...-
1/
1/
- - -it
!
i
I
I
I
i
' !
n-
cP-
,
I
1
I
I..••
L.-
r'1
,"
I
I
I
!
.
7 8
```