In a projective plane P(E) where E is a vector space of dimension 3 over any field K, a conic is these to f points of homogeneous coordinates (x,y,z) such that Where   We can write the equation of the...

In a projective plane P(E) where E is a vector space of dimension 3 over any field K, a conic is these to f points of homogeneous coordinates (x,y,z) such that

Where
  We can write the equation of the conic as

And letting

The equation of the conic becomes