Geometri Gymnasiematematik(high school math) matematik 2c

Conical sections


The force of gravity determines the trajectories of the celestial bodies. Mathematical analysis reveals that there are three types of trajectories possible for a body moving in a gravitational field determined by Newton’s law of gravity.

  • If one of the bodies has very high speed relative to the other the moving body traces out a hyperbola. The equation for this is
    x 2/a2 – y 2/b=1
  • If the speeds of the bodies are beelow a certain threshold value they move in an elliptical curve. x 2/a2 + y 2/b2 =1
  • The limiting case between the hyperbola and the ellipse is the parabola. y=ax

Those geometrical objects can be illustrated by slicing the cone according to the figure above.