When one of these constructs is traced out pictorially, there will exist one or two Dandelin Spheres tangent to the plane that traced it out. Studied in antiquity by Apollonius of Perga, in the two body problem, if the center of mass is assumed to be at rest, the paths of the bodies will follow one of these paths. In polar coordinates, they take th
When one of these constructs is traced out pictorially, there will exist one or two Dandelin Spheres tangent to the plane that traced it out. Studied in antiquity by Apollonius of Perga, in the two body problem, if the center of mass is assumed to be at rest, the paths of the bodies will follow one of these paths. In polar coordinates, they take the form of l over the quantity one plus e times cosine of theta, where l is the semi-latus rectum and e is the eccentricity. For 10 points, name these mathematical curves that include the ellipse, parabola, and hyperbola.
When one of these constructs is traced out pictorially, there will exist one or two Dandelin Spheres tangent to the plane that traced it out.
{Conic} Sections