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How to find the standard form and center of the circle.

How To Find The Standard Form And Center Of The Circle class=

Sagot :

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).

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