IgweMatics
The general form is:
Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0
Check the values of A, B, and C:
Circle: A = C and B = 0
Ellipse: A ≠ C but same sign, and B = 0
Parabola: Only one variable is squared (either x^2 or y^2)
Hyperbola: A and C have opposite signs, and B = 0
You can also use this trick:
Discriminant = B^2 - 4AC
If it's 0 → Parabola
If it's less than 0 → Circle or Ellipse
If it's greater than 0 → Hyperbola