- #1
Somefantastik
- 230
- 0
[tex]x^{2}-y^{2}-2x+4y+5;[/tex]
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?
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?