Plane curves of 2. order (conic sections) treated by their invariants.
The article Invariants of curves of second order treats conic sections as algebraic curves by their invariants.
Determining the invariants of curves of second order
a11x2 +2a12xy + a22y2 + 213x +2a23y + a33 = 0
from the coefficients $aik$ of the equation is a well known task.
We derive formulas for the invariants following an elementary high school
course developed by Freudenthal and Heinrich 50 years ago.