10.9 Polar Equations of Conics

The focus of all conics in polar graphs are at the pole.

Parabola with its directrix

Equations for Conics in Polar Graphs

Depending on if the directrix is

horizontal or vertical

eSin

epror

eCos

epr

11

LeftRight

DirectrixVertical

, BelowAbove

DirectrixHorizontal

,

Remember what “e” stand for in Conics

e is for eccentricity, which is a ratio of c/a

c is the distance from a focus to the center

a is the distance from a vertices to the center

a

cecc

a

c

Focus

vertex

p is the distance from the pole to the directrix

eSin

epror

eCos

epr

11

p

2

0

How to Indentify Conics by e

Depend on the value of e

1

10

1

eHyperbola

eEllipse

eParabola

Identify and Graph

Remember the equations eSin

epror

eCos

epr

11

Cosr

2

2

Identify and Graph

Remember the equations eSin

epror

eCos

epr

11

Ellipsee

CosCosr

,21

211

1

2

2

Identify and GraphMake a chart Ellipse

Cosr ,

211

1

30,76.1

300,33.1

150,70.

Write the equation

Hyperbola with e = 3 and directrix of x = 2

Vertical directrix

on the right of

the pole

The pole is 2 units from x = 2

p = 2

eCos

epr

1

Write the equation

Hyperbola with e = 3; p = 2

Cosr

)3(1

)2(3

Cosr

31

6

Now for a video

• http://www.youtube.com/watch?v=zV6buIBpuJo

Homework

Page 768 –

# 1, 5, 9, 13,

17, 21, 27,

31,35

Homework

Page 768 –

# 7, 11, 18,

22, 34, 36