Standard Conics

A conic is a two dimensional object. It is the set of all those points whose distance from a fixed point F is a constant times (e) its distance from a fixed straight line L.The fixed point F is called the focus, the fixed straight line is called the directrix and the fixed ratio is called the eccentricity of the conic.

If the focus is F(x1,y1) , directrix is ax+ by + c = 0 and the eccentricity is e then
√[(x - x1)2 + (y - y1)2] =e (ax + by + c)/[√(a2 + b2)]
When the focus does not lie on the conic we get non-degenerate conics. The shape of the conic depends on the value of e.
  • if e < 1 then the conic is an ellipse.
  • if e = 1 then the conic is a parabola.
  • if e > 1 then the conic is a hyperbola.