A comet follows the hyperbolic path described by #x^2/4 -y^2/19 = 1#, where x and y are in millions of miles. If the sun is the focus of the path, how close to the sun is the vertex of the path?
Unit of distance is 1 million miles.
Semi-transverse axis a = 2, semi-conjugate axis
So, the eccentricity of the hyperbola
The least distance of the comet from the Sun
= the distance between the branch vertex and its focus
The path of a comet might be nearly parabolic, with eccentricity
The whole path is unlikely to be a hyperbola, with orbital period