According to​ Kepler's first​ law, a comet should have an​elliptic, parabolic, or hyperbolic orbit​ (with gravitationalattractions from the planets​ ignored). In suitable polar​coordinates, the position left parenthesis r comma script thetaright parenthesis of a comet satisfies an equation of the form r =betaplus​e(r*cosine script theta​), where beta is a constant and eis the eccentricity of the​ orbit, with 0less than or equals lessthan1 for an​ ellipse, e equals1 for a​ parabola, and e greaterthan1 for a hyperbola. Suppose observations of a newly discoveredcomet provide the data below. Determine the type of​ orbit, andpredict where the comet will be when script theta equals 4.1 leftparenthesis radians right parenthesis. script theta 0.88 1.14 1.481.72 2.17 r 3.68 3.08 2.08 1.06 0.54 The comet has either a.hyperbolic b parabolic c elliptic  orbit. When scriptthetaequals4.1 ​(radians), the comet will be at requalsnothing.
