[tex]x^{2}-y^{2}-2x+4y+5;[/tex](adsbygoogle = window.adsbygoogle || []).push({});

let [tex]x^{2}-y^{2}-2x+4y+5 \ = \ c; [/tex]

To sketch this as a level curve, I'm not sure how to proceed. I can't seem to rearrange the function into anything familiar.

For the sake of trying to find a reference point, I let x=0 and found

[tex] y \ = \ 2 \ ^{+}_{-}\sqrt{9-c};[/tex]

then y=0 =>

[tex] x \ = \ 1 \ ^{+}_{-}\sqrt{-4+c};[/tex]

If I let c = 5, I get

[tex]x^{2}-y^{2}-2x+4y = 0; [/tex]

which gives x = 0, x = 2, y = 0, y = 4.

What should I do next?

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# Sketching level curves

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