Concept:
The standard forms of the equations of the conic sections, shown to the right, can all be written in the general form:
Ax2 + Cy2 + Dx + Ey + F = 0
This equation is a simplification of
Ax2 + Bxy + Cy2 + Dx + Ey + F = 0
with B = 0 so that the xy term of the equation vanishes.
parabola
y = a(x - h)2 + k
x = a(y - k)2 + h
circle (x - h)2 + (y - k)2 = r2
ellipse (x - h)2 + (y - k)2 = 1
a2b2
(x - h)2 - (y - k)2 = 1
hyperbola a2b2 (y - k)2 - (x - h)2 = 1
b2a2
x = a(y - k)2 + h
circle (x - h)2 + (y - k)2 = r2
ellipse (x - h)2 + (y - k)2 = 1
a2b2
(x - h)2 - (y - k)2 = 1
hyperbola a2b2 (y - k)2 - (x - h)2 = 1
b2a2
