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.
which of the following are homeomorphic?
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$\begingroup$
general-topology
analytic-geometry
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2Those are not in general form (no mixed terms). So you only need to complete squares. – 2012-07-19
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0You could plot them on Wolfram Alpha. – 2012-07-19
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0Thank 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 $c$ – 2012-07-19
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0Hint for (c): $x^2 - 2 x + 1 = (x-1)^2$ – 2012-07-19
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2@Patience, please get some graph paper and draw some pictures. This is upsetting. – 2012-07-19
1 Answers
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A is a circumference in a. and b. while a disk in c. so...
a. Yes, homeomorphism by isometric transformation to overlay the centers, and then by projection of one onto the other.
b. No, the circumference is compact, while the hyperbola is not
c. No, same reason as b