Polar form of Conic SectionsWarm Up: Graph r = -4cosθ, what is the conic section is it? What are the coordinates of its center in both polar & rectangular form?

Polar Equations of ConicsThe graph of a polar equation of the form

is a conic, where e > 0 is the eccentricity and |p| is the distance between the focus (pole) and the directrix.

Note: For an ellipse e <1

For a parabola e = 1

For a hyperbola e >1 where e = PF/PQ

PF = distance from any point to the focus

PQ = distance from the same point to the directrix

1 cos 1 sin

ep epr or r

e

Matching Orientation to the correct version of the formula

F

P (r, θ)

1 cos

epr

e

Matching Orientation to the correct version of the formula

F

P (r, θ)

1 cos

epr

e

Matching Orientation to the correct version of the formula

F

P (r, θ)

1 sin

epr

e

Matching Orientation to the correct version of the formula

F

P (r, θ)

1 sin

epr

e

Identify the conic section & graph

15

3 2cosr

Find the equation of a parabola with focus at the pole and a directrix of y = 3

Identify the conic section & graph

32

3 5sinr

Find the equation in polar form of the ellipse with focus at the pole with vertices (2, π/2) & (4, 3π/2)