# which of the following are homeomorphic?

well, I have forgotten how to identify ellipse, hyperbola,circle straightline from the general equation of conic, so is there any other way to identify these homeomorphic or not? a) B is an ellipse, b) B is an hyperbola, c) B is an complement of a closed ellipse. please help.

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Those are not in general form (no mixed terms). So you only need to complete squares. –  azarel Jul 19 '12 at 20:13
You could plot them on Wolfram Alpha. –  Rudy the Reindeer Jul 19 '12 at 20:18
Thank you for the comment of azrael, I have calculated that $(a)$ A is an hyperbola so is not homeomorphic to B, $(b)$ both are hyperbola so homeomorphic, but still confused about $c$ –  La Belle Noiseuse Jul 19 '12 at 20:19
Hint for (c): $x^2 - 2 x + 1 = (x-1)^2$ –  Robert Israel Jul 19 '12 at 20:24
@Patience, please get some graph paper and draw some pictures. This is upsetting. –  Will Jagy Jul 19 '12 at 20:38