[M] According to Kepler's first law, a comet should have an elliptic, parabolic, or hyperbolic orbit (with gravitational attractions from the planets ignored). In suitable polar coordinates, the position (r, v) of a comet satisfies an equation of the form r = B + e(r ·cos 8) where B is a constant and e is the eccentricity of the orbit, with 0 < e < 1 for an ellipse, e = 1 for a parabola, and e > 1 for a hyperbola. Suppose observations of a newly discovered comet provide the data below. Determine the type of orbit, and predict where the comet will be when & = 4.6 (radians). .88 1.10 1.42 1.77 2.14 3.00 2.30 1.65 1.25 1.01

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