Answer: [tex](x+10)^2+(y+6)^2=121[/tex]
Step-by-step explanation:
The equation of a circle in the general form is:
[tex]ax^{2}+by^2+cx+dy+e=0[/tex]
The equaton of a circle in standard form is:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Where the center is at (h, k) and r is the radius
To write the equation of a circle from general form to standard form, you must complete the squaare, as you can see below:
1- Given the equation in general form:
[tex]x^{2}+y^2+20x+12y+15=0[/tex]
2- Complete the square:
-Group the like terms and move the constant to the other side.
- Complete the square on the left side of the equation.
- Add the same value to the other side.
Then you obtain:
[tex](x^{2}+20x)+(y^2+12y)=-15\\(x^2+20x+(\frac{20}{2})^2)+(y^2+12y+(\frac{12}{2})^2)=-15+(\frac{20}{2})^2+(\frac{12}{2})^2\\\\(x+10)^2+(y+6)^2=-15+100+36\\(x+10)^2+(y+6)^2=121[/tex]
