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circle s
(x-h)2+(y-k)2=r2
parabola s up
(x-h)2=4a(y-k)
parabola s side
(y-k)2=4a(x-h)
ellipse s
(x-h)2/a2 + (y-k)2/b2 =1
hyperbola s
(x-h)2/a2 - (y-k)2/b2 =1
circle g
a=c
parabola g
a is 0 or c is 0
ellipse g
a doesn’t equal c and same sign
hyperbola g
a and c are opposite signs
general
ax2+cx2+dx+ex+f=0