CONIC SECTIONS APPLICATIONS

      The parabola has an electromagnetic signal reflection property.  Four signals are shown in green and blue.  These  signals are shown with arrows on both ends to indicate the focus either collects the signals (coming in) or the focus generates the signals and they leave in parallel from the parabola.  The inside of the parabola can be a mirror (for light) or another material  (for non visible electromagnetic waves.)

       As light enters parallel to axis of symmetry it will strike the parabola and reflect toward the focus.  You can see heavy black line segments drawn on the parabola on the lines tangent to the parabola at the points of incidence.  Two angles are formed between each of these segments and the light striking and bouncing off; each pair of angles are equal and depend upon the location the light hits the parabola. 

      Imagine the focus is a light bulb and the parabola a mirror.  The light bulb emits light in all directions.  All the light that strikes the parabola will leave parallel to the axis of symmetry.  Spot lights make use of this property. 

     Of course a a parabolic mirror is 3-dimensional.  Imagine rotating the parabola about its axis of symmetry and you will get a shape you'll recognize as the headlight of your car.

Light emitted from the focus leaves the parabolic mirror in parallel paths, shown below. Headlights, spotlights, etc., have the shape of a parabola to increase the intensity of the light  and direct the light.

The parabola also amplifies any signal entering it directing it to the focus.   Satellite dishes use this property as do dishes used at astronomical observatories.

     The ellipse has similar reflective properties.  Below you see three lines, blue, green and red.  These lines start from either focus and 'bounce' off the ellipse toward the other focus.  As with the parabola, the angles between each signal and its tangent line segment (dark black) are equal.

     In Orlando, Florida, there was a Science museum I would frequent with my son and wife; the John Young Science Museum.  In a very large room in that museum located at each end were the vertex sections of an ellipsoid (3d ellipse: from a 2d ellipse rotated about its major axis.)  The location of each focus was marked on the floor.  I would stand at one focus and my wife and son would stand at the other.  The distance between the two was maybe 170 feet.  We could literally whisper to each other and could hear each other as if we were side by side, even though there was a significant amount of background noise due to all of the other visitors in between and around us.

     Shown below is me whispering from focus A and most of my voice gets reflected to focus  B where my son and wife would listen.  They in turn would respond with most of their voices being reflected back to me at focus A.

     The hyperbola also has a reflective property.   This property involves one branch and the other focus.  Light striking the  branch from outside that is directed at that branch's focus gets reflected to the other focus. Four examples are shown below in red, magenta and blue, and black. The tangent line segments and the equal angles for each  beam of light are shown as well.

     Oftentimes a combination of parabolas and hyperbolas are used together for dish telescopes.  The parabola requires parallel light for it to be collected at its focal point, but the hyperbola can take the signals from any direction and collect them at its focal point as (long as those signals are aimed at the other branch's focal point.)  Together, a wider spectrum of signals can be monitored.

  All three conic sections are used to describe the paths of planetary motion.  Shown below are three different paths an object can take around our sun.  The black arrows represent the objects moving along these paths.

The magnitude of its velocity and the distance form the vertex to the sun determine its path.

 v is the velocity of the object in meters per second, m/s.

 G is the universal gravitational constant:  m³/(kgsec²).

 M is the mass of the sun:  1.989x10³⁰ kg

 p  is the distance from the vertex to the focus, the sun, in meters.

(Note: not all planets, comets, etc, have the same vertex about the sun.)