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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 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)