Chapter 12.2, Problem 69SE

For the following exercises, assume an object enters our solar system and we want to graph its path on a coordinate system with the sun at the origin and the x-axis as the axis of symmetry for the objects path. Give the equation of the flight path of each object using the given information.

69. The object enters along a path approximated by the line $y=\frac{1}{3}x-1$ and passes within 1 au of the sun at its closest approach, so the sun is one focus of the hyperbola. It then departs the solar system along a path approximated by the line $y=-\frac{1}{3}x+1$ .