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