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, 8) of a comet satisfies an equation of the form =B+ e(r• cos 8), where B is a constant and e is the eccentricity of the orbit, with Ose<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 8 =4.2 (radians). 9 0.85 r 3.64 |2.17 1.05 1.14 1.42 1.74 3.02 1.98 0.58 The comet has orbit. When 8 = 4.2 (radians), the comet will be at r=. Round to two decimal places as needed.)

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