To find the equation of a circle, we use the general form of a circle's equation:
[tex]$(x - h)^2 + (y - k)^2 = r^2$[/tex]
Where [tex]\((h, k)\)[/tex] is the center of the circle and [tex]\(r\)[/tex] is the radius.
Given the center [tex]\((-5, 5)\)[/tex]:
- [tex]\(h = -5\)[/tex]
- [tex]\(k = 5\)[/tex]
And the radius [tex]\(r = 3\)[/tex].
Now, we substitute these values into the general form:
[tex]$(x - (-5))^2 + (y - 5)^2 = 3^2$[/tex]
Simplify the expression inside the parentheses:
[tex]$(x + 5)^2 + (y - 5)^2 = 9$[/tex]
So, the equation of the circle is:
[tex]$(x + 5)^2 + (y - 5)^2 = 9$[/tex]
Therefore, the correct answer is:
A. [tex]$(x+5)^2+(y-5)^2=9$[/tex]
