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Section 8-5

- Polar Equations of Conics

Focus Directrix Definition

- all conics can be defined using a special

definition (similar to the parabola definition) - a conic section is the set of all points whose

distances from a particular point (focus) and a

particular line (the directrix) have a constant

ratio - the constant ratio is the eccentricity (e)
- if e gt 1 hyperbola
- if e lt 1 ellipse
- if e 1 parabola

Focus Directrix Defintion

- let P be a point on the conic, F is the focus,

and D be the closest point on the directrix

P

D

F

the directrix

Polar Equation of Conics

- the new formula for eccentricity can be used to

derive polar equations for conics - place the focus of the conic at (0 , 0) and call

the directrix x k

P(r,?)

D

F(0,0)

x k

Polar Equation of Conics

P(r,?)

D

r

?

F(0,0)

rcos ?

x k

Polar Equations of Conics

Polar Equations of Conics

- the formula derived in the previous slide is the

polar form for a conic based on the eccentricity

(e) and a value k which comes from the directrix - there are three other formulas that are just

like it depending on the orientation of the conic

in relation to the focus and directrix - the next four slides show the four different

formula and their orientation

F(0 , 0)

directrix x k

F (0 , 0)

directrix x k

directrix y k

F(0 , 0)

F(0 , 0)

directrix y k

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