EXPLANATION:
To find the radius of a circle and then its equation we must follow the following steps:
-The center is -3 and -1 that is h and k
-The radius of the circle is Half the diameter, we can see in the graph that it is at the value of -3 that is 3
Now knowing the radius and the center we can find the canonical equation of the circumference; then (-3, -1); the radius must be positive;
h, k
[tex]\begin{gathered} (x-h)^2+(y-k)^2=r^2 \\ Now\text{ we must }replace\text{ the values }of\text{ the center and the radius}; \\ (x-(-3)^{})^2+(y-(-1))^2=(3)^2 \\ (x+3)^2+(y+1)^2=3^2\text{ " }canonical\text{ equation"} \end{gathered}[/tex]Now to obtain the standard or general equation we must solve the operations of the canonical equation that we already found; the standard equation is the following:
[tex]\begin{gathered} (x+3)^2+(y+1)^2=3^2\text{ ; }we\text{ solve in the way:}(a+b)^2=a^2+2ab+b^2 \\ x^2+6x+3^2+y^2+2y+1^2=3^2 \\ \times^2+6x+9+y^2+2y+1=9;\text{ Now }we\text{ must }order\text{ the equation} \\ x^2+y^2+6x+2y+10=9 \\ \text{ANSWER: The equation of the circle in standard form is :} \\ x^2+y^2+6x+2y+10=9 \end{gathered}[/tex]