Polar form of Conic Sections

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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 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

Matching Orientation to the correct version of the formula P (r, θ) F

Matching Orientation to the correct version of the formula P (r, θ) F

Matching Orientation to the correct version of the formula P (r, θ)

Identify the conic section & graph

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

Identify the conic section & graph

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