Polar form of Conic Sections
Warm 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 Conics
The graph of a polar equation of the form
ep
r
1  e cos 
or
ep
r
1  sin 
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
Matching Orientation to the correct
version of the formula
P (r, θ)
F
ep
r
1  e cos 
Matching Orientation to the correct
version of the formula
ep
r
1  e cos 
P (r, θ)
F
Matching Orientation to the correct
version of the formula
P (r, θ)
F
ep
r
1  e sin 
Matching Orientation to the correct
version of the formula
ep
r
1  e sin 
F
P (r, θ)
Identify the conic section & graph
15
r
3  2 cos 
Find the equation of a parabola with focus at the
pole and a directrix of y = 3
Identify the conic section & graph
32
r
3  5sin 
Find the equation in polar form of
the ellipse with focus at the pole
with vertices (2, π/2) & (4, 3π/2)