Some Comets Orbit the Sun in Elliptical Orbits with the Sun

Short Answer

Some comets orbit the sun in elliptical orbits with the sun at one focus. The path of the orbit of Halley's Comet has a major axis of length 35.8 astronomical units (AU) and an eccentricity of .967. (Source: NASA.) Position the center of the ellipse at the origin and determine the equation of the ellipse. What is the minimum distance between Halley's Comet and the sun?