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CONICS FAMILY




   Take a torch light, switch it on in a dark room.  A cone  of light starts from it and falls on the wall.

1. Hold the torch straight, a circular patch of light falls on the wall.
2. Tilt the torch's face slightly downwards, you can see a elliptical patch of light.
3. Tilt the face upwards,now parabola is visible.
4.Tilt the face still more upwards, hyperbola appears.(double curve)

  Here the light cone is sliced off by the wall at various angles and the different shapes appear.  All these curves are called conics.
     All these conics can be created by a single equation.
AX^2+BXY+CY^2+DX+EY+F = 0

    Here X and Y are graph-coordinates.  A,B,C,D.E and F are constant numbers.  By feeding suitable values to the constants, one can create any curve belonging to the conic family.  Conics are observed in many motions.

     The electrons in the atoms and the planets in the solar system orbits in a circular or elliptical path.

      Any body moving under gravity follows parabolic path.  Examples; jet of water;a kicked ball, a dropped bomb from a flight.

     Some times rocket uses a planet's gravity to propel itself and go into the space.  Here, it will follow a hyperbola path and the action is called 'slingshot.'

     These curves are natural and found everywhere.  Hence studying their geometry is highly useful.





  

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