College Preparatory Program • Saudi Aramco Conic Sections
1 of 39
Circle Example 1
Center-Radius Form
222rkyhx
General Form
022 dcybxayax
Center ( h, k )
Radius r
Domain & Range D : [Left, Right ]
D : [h-r, h+r ] *************
R : [Bottom, Top ] R : [k-r, k+r ]
************* A = πr2 units2
Circum. = 2πr units
Find Equation of Circle with r = 2 & Center (1,-3)
43122 yx 066222 yxyx ( 1, -3 ) 2
D : [ -1, 3] R : [ -5, -1]
A = 4π units2 Circum. = 4π units
College Preparatory Program • Saudi Aramco Conic Sections
2 of 39
Circle Example
2
Center-Radius Form
222rkyhx
General Form
022 dcybxayax
Center ( h, k )
Radius r
Domain & Range D : [Left, Right ]
D : [h-r, h+r ] *************
R : [Bottom, Top ] R : [k-r, k+r ]
************* A = πr2 units2
Circum. = 2πr units
Find Equation of Circle with d = 6 & Center (3,-1)
91322 yx 012622 yxyx ( 3, -1 ) 3
D : [ 0, 6] R : [ -4, 2]
A = 9π units2 Circum. = 6π units
College Preparatory Program • Saudi Aramco Conic Sections
3 of 39
Circle Example 3
Center-Radius Form
222rkyhx
General Form
022 dcybxayax
Center ( h, k )
Radius r
Domain & Range D : [Left, Right ]
D : [h-r, h+r ] *************
R : [Bottom, Top ] R : [k-r, k+r ]
************* A = πr2 units2
Circum. = 2πr units
Find Equation of Circle with diameter endpoints
P(-1,2) & Q(5,8)
185222 yx
01110422 yxyx
( 2, 5 ) 18
D : [ 2- 18 , 2+ 18 ]
R : [5- 18 , 5+ 18 ]
A = 18π units2
Circum. = 6π 2 units
College Preparatory Program • Saudi Aramco Conic Sections
4 of 39
Circle Example 4
Center-Radius Form
222rkyhx
General Form
022 dcybxayax
Center ( h, k )
Radius r
Domain & Range D : [Left, Right ]
D : [h-r, h+r ] *************
R : [Bottom, Top ] R : [k-r, k+r ]
************* A = πr2 units2
Circum. = 2πr units
Find Equation of Circle with center (1,-1)
containing (-5,3) 5211
22 yx 0502222 yxyx ( 1, -1 ) 52
D : [ 1- 52 , 1+ 52 ]
R : [-1- 52 ,-1+ 52 ]
A = 52π units2
Circum. = 2π 52 units
College Preparatory Program • Saudi Aramco Conic Sections
5 of 39
Circle Example 5
Center-Radius Form
222rkyhx
General Form
022 dcybxayax
Center ( h, k )
Radius r
Domain & Range D : [Left, Right ]
D : [h-r, h+r ] *************
R : [Bottom, Top ] R : [k-r, k+r ]
************* A = πr2 units2
Circum. = 2πr units
Write the following circle in General Form
213222 yx
213222 yx
086422 yxyx ( 2, -3 ) 21
D : [ 2- 21 , 2+ 21 ]
R : [-3- 21 ,-3+ 21 ] A = 21π units2
Circum. = 2π 21 units
College Preparatory Program • Saudi Aramco Conic Sections
6 of 39
Circle Example 6
Center-Radius Form
222rkyhx
General Form
022 dcybxayax
Center ( h, k )
Radius r
Domain & Range D : [Left, Right ]
D : [h-r, h+r ] *************
R : [Bottom, Top ] R : [k-r, k+r ]
************* A = πr2 units2
Circum. = 2πr units
Write the following circle in Center-Radius Form
0178622 yxyx
424322 yx
0178622 yxyx ( 3, -4 ) 42
D : [ 3- 42 , 3+ 42 ]
R : [-4- 42 ,-4+ 42 ] A = 42π units2
Circum. = 2π 42 units
College Preparatory Program • Saudi Aramco Parabolas
7 of 39
Parabola Examples
GENERALIZATIONS a = squared coeff. b=linear
coefficient c=constant
4p
1a means
4a
1p
# TYPES DIRECTION FORMAT VERTEX FOCUS DIRECTRIX AXIS DOMAIN RANGE
1 02 awithcbxaxy Up 2hxky4p (h , k) (h , k+p) y=k-p x=h [k, + ∞)
2 02 awithcbxaxy Down 2hxky4p (h , k) (h , k-p) y=k+p x=h (-∞, k]
3 02 awithcbyayx Right 2kyhx4p (h , k) (h+p , k) x=h-p y=k [h, + ∞)
4 02 awithcbyayx Left 2kyhx4p (h , k) (h-p , k) x=h+p y=k (-∞, h]
hxAxis
pkyDDOWN
pkhFa
pkyDUP
pkhFa
ap
khVertex
hfk
a
bh
:
:&
,0
:&
,0
4
1
,
2
kyAxis
phxDLEFT
kphFa
phxDRIGHT
kphFa
ap
khVertex
kuh
a
bk
:
:&
,0
:&
,0
4
1
,
2
Vertical Parabola Horizontal Parabola
College Preparatory Program • Saudi Aramco Parabolas
8 of 39
Parabola Example 1
# Example Direction Format Vertex Focus Directrix Axis Domain Range
1 342 xxy Up 2211 xy 1,2
4
3,2
4
5y 2x ,1
College Preparatory Program • Saudi Aramco Parabolas
9 of 39
Parabola Example 2
# Example Direction Format Vertex Focus Directrix Axis Domain Range
2 633 2 xxy Up
2
2
1
4
27
3
1
xy
4
27,
2
1
3
20,
2
1
6
41y
2
1x
,
4
27
College Preparatory Program • Saudi Aramco Parabolas
10 of 39
Parabola Example 3
# Example Direction Format Vertex Focus Directrix Axis Domain Range
3 82 2 xy Up 208
2
1 xy 8,0
8
63,0
8
65y
0x ,8
College Preparatory Program • Saudi Aramco Parabolas
11 of 39
Parabola Example 4
# Example Direction Format Vertex Focus Directrix Axis Domain Range
4 Vertical Parabola with
vertex (1,-2) containing (0, -1)
Up 2121 xy 2,1
4
7,1
4
9y 1x ,2
College Preparatory Program • Saudi Aramco Parabolas
12 of 39
Parabola Example 5
# Example Direction Format Vertex Focus Directrix Axis Domain Range
5 322 2 yyx Left
2
2
1
2
5
2
1
yx
2
1,
2
5
2
1,
8
21
8
19x
2
1y
2
5,
College Preparatory Program • Saudi Aramco Parabolas
13 of 39
Parabola Example 6
# Example Direction Format Vertex Focus Directrix Axis Domain Range
6 642 yyx Right 2221 yx 2,2
2,
4
9 4
7x 2y ,2
College Preparatory Program • Saudi Aramco Ellipses
14 of 39
Ellipse Examples
Example
VERTEX FORMS
RLgoesMinor
DUgoesMajor
a
ky
b
hx
a
y
b
x
ba
DUgoesMinor
RLgoesMajor
b
ky
a
hx
b
y
a
x
ba
&
&
1
1
***************
&
&
1
1
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
GENERAL FORM
022 edycxbyax
)/(""
)/(""
: 22
DUcmeansxy
RLcmeansyx
bacFC
DenDen
DenDen
CENTER
( h, k )
***** (Foci)
L/R :
(h-c,k) & (h+c,k)
***** U/D :
(h,k-c) & (h,k+c)
VERTICES (ENDPTS.
OF MAJOR)
L/R (h-a,k) & (h+a,k)
***** U/D :
(h,k-a) & (h,k+a)
(ENDPTS.
OF MINOR)
L/R (h-b,k) & (h+b,k)
***** U/D :
(h,k-b) & (h,k+b)
bkhbkh
DU
goEndptsMinor
kchkchF
kahkahME
RLgo
FociEndptsMajor
bac
b
ky
a
hx
b
y
a
x
,&,
&
.
,&,:
,&,:
&
&.
1
1
22
2
2
2
2
2
2
2
2
kbhkbh
RL
goEndptsMinor
ckhckhF
akhakhME
DUgo
FociEndptsMajor
bac
a
ky
b
hx
a
y
b
x
,&,
&
.
,&,:
,&,:
&
&.
1
1
22
2
2
2
2
2
2
2
2
Horizontal Ellipse Vertical Ellipse
College Preparatory Program • Saudi Aramco Ellipses
15 of 39
Ellipse Example 1
VERTEX FORMS
RLgoesMinor
DUgoesMajor
a
ky
b
hx
a
y
b
x
ba
DUgoesMinor
RLgoesMajor
b
ky
a
hx
b
y
a
x
ba
&
&
1
1
***************
&
&
1
1
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
GENERAL FORM
022 edycxbyax
)/(""
)/(""
: 22
DUcmeansxy
RLcmeansyx
bacFC
DenDen
DenDen
CENTER
( h, k )
***** (Foci)
L/R :
(h-c,k) & (h+c,k)
***** U/D :
(h,k-c) & (h,k+c)
VERTICES (ENDPTS.
OF MAJOR)
L/R (h-a,k) & (h+a,k)
***** U/D :
(h,k-a) & (h,k+a)
(ENDPTS.
OF MINOR)
L/R (h-b,k) & (h+b,k)
***** U/D :
(h,k-b) & (h,k+b)
Fill in data for the ellipse
1259
22
yx
College Preparatory Program • Saudi Aramco Ellipses
17 of 39
Ellipse Example 2
VERTEX FORMS
RLgoesMinor
DUgoesMajor
a
ky
b
hx
a
y
b
x
ba
DUgoesMinor
RLgoesMajor
b
ky
a
hx
b
y
a
x
ba
&
&
1
1
***************
&
&
1
1
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
GENERAL FORM
022 edycxbyax
)/(""
)/(""
: 22
DUcmeansxy
RLcmeansyx
bacFC
DenDen
DenDen
CENTER
( h, k )
***** (Foci)
L/R :
(h-c,k) & (h+c,k)
***** U/D :
(h,k-c) & (h,k+c)
VERTICES (ENDPTS.
OF MAJOR)
L/R (h-a,k) & (h+a,k)
***** U/D :
(h,k-a) & (h,k+a)
(ENDPTS.
OF MINOR)
L/R (h-b,k) & (h+b,k)
***** U/D :
(h,k-b) & (h,k+b)
Fill in data for the ellipse
1
4
1
16
122
yx
College Preparatory Program • Saudi Aramco Ellipses
19 of 39
Ellipse Example 3
VERTEX FORMS
RLgoesMinor
DUgoesMajor
a
ky
b
hx
a
y
b
x
ba
DUgoesMinor
RLgoesMajor
b
ky
a
hx
b
y
a
x
ba
&
&
1
1
***************
&
&
1
1
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
GENERAL FORM
022 edycxbyax
)/(""
)/(""
: 22
DUcmeansxy
RLcmeansyx
bacFC
DenDen
DenDen
CENTER
( h, k )
***** (Foci)
L/R :
(h-c,k) & (h+c,k)
***** U/D :
(h,k-c) & (h,k+c)
VERTICES (ENDPTS.
OF MAJOR)
L/R (h-a,k) & (h+a,k)
***** U/D :
(h,k-a) & (h,k+a)
(ENDPTS.
OF MINOR)
L/R (h-b,k) & (h+b,k)
***** U/D :
(h,k-b) & (h,k+b)
Fill in data for the ellipse
011181694 22 yxyx
College Preparatory Program • Saudi Aramco Ellipses
21 of 39
Ellipse Example 4
VERTEX FORMS
RLgoesMinor
DUgoesMajor
a
ky
b
hx
a
y
b
x
ba
DUgoesMinor
RLgoesMajor
b
ky
a
hx
b
y
a
x
ba
&
&
1
1
***************
&
&
1
1
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
GENERAL FORM
022 edycxbyax
)/(""
)/(""
: 22
DUcmeansxy
RLcmeansyx
bacFC
DenDen
DenDen
CENTER
( h, k )
***** (Foci)
L/R :
(h-c,k) & (h+c,k)
***** U/D :
(h,k-c) & (h,k+c)
VERTICES (ENDPTS.
OF MAJOR)
L/R (h-a,k) & (h+a,k)
***** U/D :
(h,k-a) & (h,k+a)
(ENDPTS.
OF MINOR)
L/R (h-b,k) & (h+b,k)
***** U/D :
(h,k-b) & (h,k+b)
Fill in data for the ellipse
071850425 22 yxyx
College Preparatory Program • Saudi Aramco Ellipses
23 of 39
Ellipse Example 5
VERTEX FORMS
RLgoesMinor
DUgoesMajor
a
ky
b
hx
a
y
b
x
ba
DUgoesMinor
RLgoesMajor
b
ky
a
hx
b
y
a
x
ba
&
&
1
1
***************
&
&
1
1
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
GENERAL FORM
022 edycxbyax
)/(""
)/(""
: 22
DUcmeansxy
RLcmeansyx
bacFC
DenDen
DenDen
CENTER
( h, k )
***** (Foci)
L/R :
(h-c,k) & (h+c,k)
***** U/D :
(h,k-c) & (h,k+c)
VERTICES (ENDPTS.
OF MAJOR)
L/R (h-a,k) & (h+a,k)
***** U/D :
(h,k-a) & (h,k+a)
(ENDPTS.
OF MINOR)
L/R (h-b,k) & (h+b,k)
***** U/D :
(h,k-b) & (h,k+b)
Fill in data for the ellipse
VE, ctr (-1,2), major 10, minor 6
College Preparatory Program • Saudi Aramco Ellipses
25 of 39
Ellipse Example 6
VERTEX FORMS
RLgoesMinor
DUgoesMajor
a
ky
b
hx
a
y
b
x
ba
DUgoesMinor
RLgoesMajor
b
ky
a
hx
b
y
a
x
ba
&
&
1
1
***************
&
&
1
1
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
GENERAL FORM
022 edycxbyax
)/(""
)/(""
: 22
DUcmeansxy
RLcmeansyx
bacFC
DenDen
DenDen
CENTER
( h, k )
***** (Foci)
L/R :
(h-c,k) & (h+c,k)
***** U/D :
(h,k-c) & (h,k+c)
VERTICES (ENDPTS.
OF MAJOR)
L/R (h-a,k) & (h+a,k)
***** U/D :
(h,k-a) & (h,k+a)
(ENDPTS.
OF MINOR)
L/R (h-b,k) & (h+b,k)
***** U/D :
(h,k-b) & (h,k+b)
Fill in data for the ellipse
HE, ctr origin, major 6, foci 2
College Preparatory Program • Saudi Aramco Hyperbolas
27 of 39
Hyperbola Examples
# Example
VERTEX FORMS
RLgoesConjugate
DUgoesTransverse
b
hx
a
ky
b
x
a
y
y
DUgoesConjugate
RLgoesTransverse
b
ky
a
hx
b
y
a
x
x
term
term
&
&
1
1
0
***************
&
&
1
1
0
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
GENERAL FORMS
khxb
ay
b
am
khxb
ay
b
am
khxa
by
a
bm
khxa
by
a
bm
edycxbxay
HyperbolaVert
edycxbyax
HyperbolaHorz
2
1
2
1
2
1
22
2
1
22
0
.
0
.
)/(""0
)/(""0
:
2
2
22
DUcmeansy
RLcmeansx
bacFC
Term
Term
CENTER
( h, k )
***** (Foci)
L/R :
(h-c,k) & (h+c,k)
***** U/D :
(h,k-c) & (h,k+c)
VERTICES (ENDPTS.
OF MAJOR)
L/R (h-a,k) & (h+a,k)
***** U/D :
(h,k-a) & (h,k+a)
(ENDPTS.
OF MINOR)
L/R (h-b,k) & (h+b,k)
***** U/D :
(h,k-b) & (h,k+b)
bkhbkh
DU
goEndptsConj
kchkchF
kahkahTE
RLgo
FociEndptsTrans
bac
b
ky
a
hx
b
y
a
x
,&,
&
..
,&,:
,&,:
&
&..
1
1
22
2
2
2
2
2
2
2
2
kbhkbh
RL
goEndptsConj
ckhckhF
akhakhTE
DUgo
FociEndptsTrans
bac
b
hx
a
ky
b
x
a
y
,&,
&
..
,&,:
,&,:
&
&..
1
1
22
2
2
2
2
2
2
2
2
Horizontal Hyperbola Vertical Hyperbola
College Preparatory Program • Saudi Aramco Hyperbolas
28 of 39
Hyperbola Example 1
VERTEX FORMS
RLgoesConjugate
DUgoesTransverse
b
hx
a
ky
b
x
a
y
y
DUgoesConjugate
RLgoesTransverse
b
ky
a
hx
b
y
a
x
x
term
term
&
&
1
1
0
***************
&
&
1
1
0
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
GENERAL FORMS
khxb
ay
b
am
khxb
ay
b
am
khxa
by
a
bm
khxa
by
a
bm
edycxbxay
HyperbolaVert
edycxbyax
HyperbolaHorz
2
1
2
1
2
1
22
2
1
22
0
.
0
.
)/(""0
)/(""0
:
2
2
22
DUcmeansy
RLcmeansx
bacFC
Term
Term
CENTER
( h, k )
***** (Foci)
L/R :
(h-c,k) & (h+c,k)
***** U/D :
(h,k-c) & (h,k+c)
VERTICES (ENDPTS.
OF MAJOR)
L/R (h-a,k) & (h+a,k)
***** U/D :
(h,k-a) & (h,k+a)
(ENDPTS.
OF MINOR)
L/R (h-b,k) & (h+b,k)
***** U/D :
(h,k-b) & (h,k+b)
Fill in data for hyperbola
1259
22
yx
College Preparatory Program • Saudi Aramco Hyperbolas
30 of 39
Hyperbola Example 2
VERTEX FORMS
RLgoesConjugate
DUgoesTransverse
b
hx
a
ky
b
x
a
y
y
DUgoesConjugate
RLgoesTransverse
b
ky
a
hx
b
y
a
x
x
term
term
&
&
1
1
0
***************
&
&
1
1
0
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
GENERAL FORMS
khxb
ay
b
am
khxb
ay
b
am
khxa
by
a
bm
khxa
by
a
bm
edycxbxay
HyperbolaVert
edycxbyax
HyperbolaHorz
2
1
2
1
2
1
22
2
1
22
0
.
0
.
)/(""0
)/(""0
:
2
2
22
DUcmeansy
RLcmeansx
bacFC
Term
Term
CENTER
( h, k )
***** (Foci)
L/R :
(h-c,k) & (h+c,k)
***** U/D :
(h,k-c) & (h,k+c)
VERTICES (ENDPTS.
OF MAJOR)
L/R (h-a,k) & (h+a,k)
***** U/D :
(h,k-a) & (h,k+a)
(ENDPTS.
OF MINOR)
L/R (h-b,k) & (h+b,k)
***** U/D :
(h,k-b) & (h,k+b)
Fill in data for hyperbola
1
4
1
16
122
yx
College Preparatory Program • Saudi Aramco Hyperbolas
32 of 39
Hyperbola Example 3
VERTEX FORMS
RLgoesConjugate
DUgoesTransverse
b
hx
a
ky
b
x
a
y
y
DUgoesConjugate
RLgoesTransverse
b
ky
a
hx
b
y
a
x
x
term
term
&
&
1
1
0
***************
&
&
1
1
0
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
GENERAL FORMS
khxb
ay
b
am
khxb
ay
b
am
khxa
by
a
bm
khxa
by
a
bm
edycxbxay
HyperbolaVert
edycxbyax
HyperbolaHorz
2
1
2
1
2
1
22
2
1
22
0
.
0
.
)/(""0
)/(""0
:
2
2
22
DUcmeansy
RLcmeansx
bacFC
Term
Term
CENTER
( h, k )
***** (Foci)
L/R :
(h-c,k) & (h+c,k)
***** U/D :
(h,k-c) & (h,k+c)
VERTICES (ENDPTS.
OF MAJOR)
L/R (h-a,k) & (h+a,k)
***** U/D :
(h,k-a) & (h,k+a)
(ENDPTS.
OF MINOR)
L/R (h-b,k) & (h+b,k)
***** U/D :
(h,k-b) & (h,k+b)
Fill in data for hyperbola
0483649 22 yxyx
College Preparatory Program • Saudi Aramco Hyperbolas
34 of 39
Hyperbola Example 4
VERTEX FORMS
RLgoesConjugate
DUgoesTransverse
b
hx
a
ky
b
x
a
y
y
DUgoesConjugate
RLgoesTransverse
b
ky
a
hx
b
y
a
x
x
term
term
&
&
1
1
0
***************
&
&
1
1
0
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
GENERAL FORMS
khxb
ay
b
am
khxb
ay
b
am
khxa
by
a
bm
khxa
by
a
bm
edycxbxay
HyperbolaVert
edycxbyax
HyperbolaHorz
2
1
2
1
2
1
22
2
1
22
0
.
0
.
)/(""0
)/(""0
:
2
2
22
DUcmeansy
RLcmeansx
bacFC
Term
Term
CENTER
( h, k )
***** (Foci)
L/R :
(h-c,k) & (h+c,k)
***** U/D :
(h,k-c) & (h,k+c)
VERTICES (ENDPTS.
OF MAJOR)
L/R (h-a,k) & (h+a,k)
***** U/D :
(h,k-a) & (h,k+a)
(ENDPTS.
OF MINOR)
L/R (h-b,k) & (h+b,k)
***** U/D :
(h,k-b) & (h,k+b)
Fill in data for hyperbola
059632723616 22 yxxy
College Preparatory Program • Saudi Aramco Hyperbolas
36 of 39
Hyperbola Example
5
VERTEX FORMS
RLgoesConjugate
DUgoesTransverse
b
hx
a
ky
b
x
a
y
y
DUgoesConjugate
RLgoesTransverse
b
ky
a
hx
b
y
a
x
x
term
term
&
&
1
1
0
***************
&
&
1
1
0
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
GENERAL FORMS
khxb
ay
b
am
khxb
ay
b
am
khxa
by
a
bm
khxa
by
a
bm
edycxbxay
HyperbolaVert
edycxbyax
HyperbolaHorz
2
1
2
1
2
1
22
2
1
22
0
.
0
.
)/(""0
)/(""0
:
2
2
22
DUcmeansy
RLcmeansx
bacFC
Term
Term
CENTER
( h, k )
***** (Foci)
L/R :
(h-c,k) & (h+c,k)
***** U/D :
(h,k-c) & (h,k+c)
VERTICES (ENDPTS.
OF MAJOR)
L/R (h-a,k) & (h+a,k)
***** U/D :
(h,k-a) & (h,k+a)
(ENDPTS.
OF MINOR)
L/R (h-b,k) & (h+b,k)
***** U/D :
(h,k-b) & (h,k+b)
Fill in data for hyperbola
HH, ctr (-1,2), Trans. 6, Conj. 10
College Preparatory Program • Saudi Aramco Hyperbolas
38 of 39
Hyperbola Example
6
VERTEX FORMS
RLgoesConjugate
DUgoesTransverse
b
hx
a
ky
b
x
a
y
y
DUgoesConjugate
RLgoesTransverse
b
ky
a
hx
b
y
a
x
x
term
term
&
&
1
1
0
***************
&
&
1
1
0
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
GENERAL FORMS
khxb
ay
b
am
khxb
ay
b
am
khxa
by
a
bm
khxa
by
a
bm
edycxbxay
HyperbolaVert
edycxbyax
HyperbolaHorz
2
1
2
1
2
1
22
2
1
22
0
.
0
.
)/(""0
)/(""0
:
2
2
22
DUcmeansy
RLcmeansx
bacFC
Term
Term
CENTER
( h, k )
***** (Foci)
L/R :
(h-c,k) & (h+c,k)
***** U/D :
(h,k-c) & (h,k+c)
VERTICES (ENDPTS.
OF MAJOR)
L/R (h-a,k) & (h+a,k)
***** U/D :
(h,k-a) & (h,k+a)
(ENDPTS.
OF MINOR)
L/R (h-b,k) & (h+b,k)
***** U/D :
(h,k-b) & (h,k+b)
Fill in data for hyperbola
VH, ctr origin, Conj. 4, foci 6