Suppose that we model an object’s trajectory in the solar system by a hyperbolic path in the coordinate plane, with its origin at the sun and its units in astronomical units (AU).
The -axis is a line of symmetry of this hyperbola. The object enters in the direction of , leaves in the direction of ,
and passes within 1 AU of the sun at its closest point. Using the equations of the asymptotes, find the equation of the object’s path.