Question

An interesting application of conic section involves the orbits of comets in our solar system. Of the 610 comets identifed prior to 1970, 245 have elliptical orbits, 295 have parabolic orbits, and 70 have hyperbolic orbits. The center of the sun is a focus of each of these orbits, and each orbit has a vertex at the point where the comet is closet to the sun. Halley's Comet is a comet that repeats it orbit every 76 years. Which conic section must represent the path of its orbit? (Don't overthink this one!)

Answer 1

Notice that hyperbolas and parabolas are not closed curves. Then, whenever an object has a parabolic or a hyperbolic trajectory, it will not come back.

Nevertheless, Halley's Comet repeats its orbit each 76 years. Then, the only possibility for it is to have an elliptical orbit.

Therefore, the answer is option a) Ellipse.