how an I tell if this is a circle or an ellipse? also, how am I supposed to solve it?
-x^2+2y^2+8x+3=0
I answered a similar question for Jordan last night at 11:20
divide your equation by -1 to make it start with a positive x^2 term.
At this point you should realize that it is neither a circle nor an ellipse, but rather a hyperbola.
Follow the same steps.
put it in standard form.
for the x, complete the square
(x-k)^2/a^2 + (y-h)^2/b^2 =1
if a an b are equal, it is a circle