# Thread: How would I complete the square for this equation?

1. ## How would I complete the square for this equation?

$\displaystyle x^2+y^2-2x+4y=-6$

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2. Originally Posted by deathtolife04
$\displaystyle x^2+y^2-2x+4y=-6$

?
piece by piece.

rewrite as: $\displaystyle \left( x^2 - 2x \right) + \left( y^2 + 4y \right) = -6$

and complete the square for what's in the brackets separately (that is, complete the square for the x's and complete the square for the y's), then simplify

3. Originally Posted by Jhevon
piece by piece.

rewrite as: $\displaystyle \left( x^2 - 2x \right) + \left( y^2 + 4y \right) = -6$

and complete the square for what's in the brackets separately (that is, complete the square for the x's and complete the square for the y's), then simplify
thanks!

ok so $\displaystyle (x-1)(x-1) + (y+2)(y+2) = -1$

I have been told that my original equation was invalid. But just by looking at $\displaystyle (x-1)(x-1) + (y+2)(y+2) = -1$, couldn't I call that a circle?

4. Yes, you have some problems, there. Who told you it was a circle? It's not necessarily invalid, unless it's supposed to be a circle. Where did you get it and what was the original problem statement?

5. Originally Posted by deathtolife04
thanks!

ok so $\displaystyle (x-1)(x-1) + (y+2)(y+2) = -1$

I have been told that my original equation was invalid. But just by looking at $\displaystyle (x-1)(x-1) + (y+2)(y+2) = -1$, couldn't I call that a circle?
you could have written: $\displaystyle (x - 1)^2 + (y + 2)^2 = -1$

this is not a circle (unless you made an error), since we could not have a negative number on the right hand side if it were a circle.

unless maybe the circle has a radius in the complex plane, but i don't think that makes sense, never did complex analysis

6. Originally Posted by Jhevon
you could have written: $\displaystyle (x - 1)^2 + (y + 2)^2 = -1$

this is not a circle (unless you made an error), since we could not have a negative number on the right hand side if it were a circle.

unless maybe the circle has a radius in the complex plane, but i don't think that makes sense, never did complex analysis

ok, i guess i'll just write "imaginary circle" then...

7. Originally Posted by deathtolife04
ok, i guess i'll just write "imaginary circle" then...
i wouldn't recommend that. are you sure it wasn't a typo. as far as i've seen, the instructions did not ask you to identify the curve, so you don't have to say anything really

8. Originally Posted by TKHunny
Yes, you have some problems, there. Who told you it was a circle? It's not necessarily invalid, unless it's supposed to be a circle. Where did you get it and what was the original problem statement?

9. Originally Posted by Jhevon
i wouldn't recommend that. are you sure it wasn't a typo. as far as i've seen, the instructions did not ask you to identify the curve, so you don't have to say anything really

well the question just says: classify the following as the equation of a line, parabola, ellipse, hyperbola, or circle

this is the same review that my online home school has been using for years and years, and I have no way of knowing if it's a typo...

10. Probably will, 'cause it's really counterproductive a circle with a negative radius

11. Originally Posted by deathtolife04
well the question just says: classify the following as the equation of a line, parabola, ellipse, hyperbola, or circle

this is the same review that my online home school has been using for years and years, and I have no way of knowing if it's a typo...
well, it's none of those if it's of the form $\displaystyle (x - h)^2 + (y - k)^2 = c$ where $\displaystyle c < 0$

so maybe "none" is an option. i vaguely remember something about "degenerate conics" but i'm not sure if this applies here. could you say "degenerate circle" i don't know and very much doubt it

12. Originally Posted by Jhevon
well, it's none of those if it's of the form $\displaystyle (x - h)^2 + (y - k)^2 = c$ where $\displaystyle c < 0$

so maybe "none" is an option. i vaguely remember something about "degenerate conics" but i'm not sure if this applies here. could you say "degenerate circle" i don't know and very much doubt it
no it doesn't give that as an option. hopefully it's just a typo...