Question

Write equation in standard form. x^2 + y^2 +2x -2y + 2 = 36

Answer 1

complete the square for x and y

Answer 2

How would you do that

Answer 3

x^2+2x+y^2-2y=34
x^2+2x+1+y^2-2y+1=34+1+1
adding one for each to complete the square
(x+1)^2+(y-1)^2=36
(x+1)^2+(y-1)^2=6^2

Answer 4

that would be the standard form of a circles equation
(x-a)^2+(y-b)^2=r^2
with center (a,b) and radius r

Answer 5

so to summarize what i did:
- rearranged x's and y's to be together
- subtracted the constants from both side so we have only unknowns in one side
-looked at what i needed to add so to complete the square looking at 2x
which is in the form 2ab in the formula (a+b)^2=a^2+2ab+b^2
although you don't see it but 1 is in there so it is like 2(1)x which the form 2ab
- lastly completed the square and got the standard form

Answer 6

well i did the same with y just so you are not confused

Answer 7

\[x^2 + y^2 +2x -2y + 2 = 36\]Group all the x terms and y terms separately. \[(x^2+2x)+(y^2-2y)+2=36\] Send the 2 to the other side of the equation. \[(x^2+2x)+(y^2-2y)=34\]Complete the square by solving for the quadratic function, \(ax^2+bx+c\) by finding your c value. C value is found by the equation: \[c=\left(\frac{b}{2}\right)^2\] Find your `c` value for each quadratic in x and in y. \[(x^2+2x\color{red}{+1})+(y^2-2y\color{red}{+1})=34\color{red}{+1+1}\]Simplify both sides. \[(x+1)^2+(y-1)^2=36\]

To simplify your quadratic, it is essentially:\[\left(x\pm \frac{b}{2}\right)^2~,~ \left(y\pm \frac{b}{2}\right)^2\]