There are 3 types of conics: parabola, ellipse, and hyperbola.
Equation of a parabola: y = a(x - h)² + k or x = a(y - k)² + h
Equation of an ellipse: [tex]\frac{(x-h)^{2}}{a} +\frac{(y-k)^{2}}{b} =1[/tex]
Equation of a hyperbola: [tex]\frac{(x-h)^{2}}{a} -\frac{(y-k)^{2}}{b} =1[/tex]
The general equation for all of them is:
Ax² + Bxy + Cy² + Dx + Ey + F = 0 ; A, B, C, D, E, F ∈ Integers