4) Halley’s comet follows an elliptical orbit with the sun as one of the foci. The eccentricity of the orbit is approximately 0.967. The length of the major axis of the orbit is approximately 35.88 astronomical units. (An astronomical unit is about 93 million miles.)
a. Find an equation of the orbit. Let the origin represent the sun and use the x axis as the major axis.
b. Find the greatest and least distances (the aphelion and perihelion, respectively) from the sun’s center to the comet’s center.