TGiven:
[tex]x^2+y^2+8x+22y+37=0[/tex]
To determine the equation in standard form, we first rewrite x^2+y^2+8x+22y+37=0 into:
[tex]\begin{gathered} x^2+y^2+8x+22y+37=0 \\ x^2+y^2+8x+22y=-37 \\ (x^2+8x)+(y^2+22y)=-37 \\ Convert\text{ x and y into square form} \\ (x^2+8x+16)+(y^2+22y+121)=-37+16+121 \\ Simplify \\ (x+4)^2+(y+11)^2=100 \end{gathered}[/tex]
We also note the circle equation rule as shown below:
For (x-a)^2+(y-b)^2=r^2, the center is at (a,b).
Therefore, the standard form is:
[tex](x+4)^{2}+(y+11)^{2}=100[/tex]
And, the center is at the point (-4,-11).
