Pre-Calc/Chapter 8: Analytic Geometry in Two- and Three-Dimensions/8.3 Hyperbolas/8.3.6 Solve Apps: Hyperbolas Solve the problem.A comet follows the hyperbolic path described by  -   = 1, ... Solve the problem.

A comet follows the hyperbolic path described by  -   = 1, where x and y are in millions. If the sun is the focus of the path, how close to the sun is the vertex of the path?
  ]]> 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 1.0000000 0.3333333 0 true true abc 2 million Incorrect 20 million Incorrect 4.5 million Incorrect 2.5 million Correct