Question

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Answer 1

a good picture might help
http://www.wolframalpha.com/input/?i=x^2+%3D+1%2Fy^2+

Answer 2

i think you are supposed to replace \(x\) by \(-x\) and see if you get the same thing, which of course you do
you also get the same thing if you replace \(y\) by \(-y\) and also if you make both replacements
in any case is it about as symmetric as you can get