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)

D : [ ______, ______] R : [ ______, ______]

A = ______ units2 Circum. = _____

units

2 4 6 8 10-2-4-6-8-10

x

2

4

6

8

10

-2

-4

-6

-8

-10

y

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)

D : [ ______, ______] R : [ ______, ______]

A = ______ units2 Circum. = _____

units

2 4 6 8 10-2-4-6-8-10

x

2

4

6

8

10

-2

-4

-6

-8

-10

y

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)

D : [ ______, ______] R : [ ______, ______]

A = ______ units2 Circum. = _____ units

2 4 6 8 10-2-4-6-8-10

x

2

4

6

8

10

-2

-4

-6

-8

-10

y

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)

D : [ ______, ______] R : [ ______, ______]

A = ______ units2 Circum. = _____ units

2 4 6 8 10-2-4-6-8-10

x

2

4

6

8

10

-2

-4

-6

-8

-10

y

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

D : [ ______, ______] R : [ ______, ______]

A = ______ units2 Circum. = _____ units

2 4 6 8 10-2-4-6-8-10

x

2

4

6

8

10

-2

-4

-6

-8

-10

y

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

D : [ ______, ______] R : [ ______, ______]

A = ______ units2 Circum. = _____ units

2 4 6 8 10-2-4-6-8-10

x

2

4

6

8

10

-2

-4

-6

-8

-10

y

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

1 2 3 4 5-1-2-3-4-5

x

1

2

3

4

5

-1

-2

-3

-4

-5

y

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

1 2 3 4 5-1-2-3-4-5

x

1

2

3

4

5

-1

-2

-3

-4

-5

y

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

1 2 3 4 5-1-2-3-4-5

x

1

2

3

4

5

-1

-2

-3

-4

-5

y

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)

1 2 3 4 5-1-2-3-4-5

x

1

2

3

4

5

-1

-2

-3

-4

-5

y

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

1 2 3 4 5-1-2-3-4-5

x

1

2

3

4

5

-1

-2

-3

-4

-5

y

College Preparatory Program • Saudi Aramco Parabolas

13 of 39

Parabola Example 6

# Example Direction Format Vertex Focus Directrix Axis Domain Range

6 642 yyx

1 2 3 4 5-1-2-3-4-5

x

1

2

3

4

5

-1

-2

-3

-4

-5

y

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

16 of 39

5 10-5-10

x

5

10

-5

-10

y

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

18 of 39

5 10-5-10

x

5

10

-5

-10

y

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

20 of 39

5 10-5-10

x

5

10

-5

-10

y

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

22 of 39

5 10-5-10

x

5

10

-5

-10

y

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

24 of 39

5 10-5-10

x

5

10

-5

-10

y

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 Ellipses

26 of 39

5 10-5-10

x

5

10

-5

-10

y

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

29 of 39

5 10-5-10

x

5

10

-5

-10

y

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

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College Preparatory Program • Saudi Aramco Hyperbolas

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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

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-5

-10

y

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

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5

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-5

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y

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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

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10

-5

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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

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x

5

10

-5

-10

y