A hedge is to be constructed in the shape of a hyperbola near a fountain at the center of a yard. The hedge will follow the asymptotes and , and its closest distance to the center fountain is 20 yards. Find the equation of the hyperbola.
Suppose that we model an object’s trajectory in the solar system by a hyperbolic path in the coordinate plane. The -axis is a line of symmetry of this hyperbola. The object enters in the direction of and leaves in the direction . The sun is positioned at the origin and the object passes within 1 AU (astronomical unit) of the sun at its closest. Using the asymptote’s equations, find the equation of the object’s path.