>0 hyperbola, <0 ellipse, =0 parabola
unless it's a degenerate form such as
2 intersecting lines, a point, 2 lines
1 b^2 -ac = 2^2-2(8) =-12 <0 ellipse
2 b^2 -ac = 1^2 = 1 >0, hyperbola
3 is a another hyperbola, b^2 -ac =0^2 -(1)(-1)= 1 >0
x^2 - y^2 = -4
y^2 -x^2 = 4
y^2/2^2 - x^2/2^2 = 1
in y^2/a^2 -x^2/b^2 = 1 form
c^2 = a^2 +b^2, c =sqr8= 2sqr2
2 branches of the hyperbola are above and below the x axis
asymptotes are y=x and y=-x
mid point between the 2 branches is the origin
vertices are (0,2) and (0,-2)
foci are (0,2sqr2) and (0,-2sqr2)
