Polar form of Conic Sections

1
Polar form of Conic Sections
Warm Up Graph r -4cos?, what is the conic
section is it? What are the coordinates of its
center in both polar rectangular form?
2
Polar Equations of Conics

• The graph of a polar equation of the form
• is a conic, where e gt 0 is the eccentricity
  and p is the distance between the focus (pole)
  and the directrix.
• Note For an ellipse e lt1
• For a parabola e 1
• For a hyperbola e gt1 where e PF/PQ
• PF distance from any point to the focus
• PQ distance from the same point to the directrix

3
Matching Orientation to the correct version of
the formula
P (r, ?)
F
4
Matching Orientation to the correct version of
the formula
P (r, ?)
F
5
Matching Orientation to the correct version of
the formula
P (r, ?)
F
6
Matching Orientation to the correct version of
the formula
F
P (r, ?)
7
Identify the conic section graph
8
Find the equation of a parabola with focus at the
pole and a directrix of y 3
9
Identify the conic section graph
10
Find the equation in polar form of the ellipse
with focus at the pole with vertices (2, p/2)
(4, 3p/2)