To determine the equation of a circle in standard form given its center and radius, we follow a specific formula. The standard form of the equation of a circle is:
[tex]\[
(x - h)^2 + (y - k)^2 = r^2
\][/tex]
Where:
- [tex]\((h, k)\)[/tex] represents the coordinates of the center of the circle.
- [tex]\(r\)[/tex] represents the radius of the circle.
Given:
- The center of the circle is at (13, -8).
- The radius of the circle is 7.
Let's plug these values into the standard form equation.
1. Identify [tex]\(h\)[/tex], [tex]\(k\)[/tex], and [tex]\(r\)[/tex]:
- [tex]\(h = 13\)[/tex]
- [tex]\(k = -8\)[/tex]
- [tex]\(r = 7\)[/tex]
2. Substitute the values into the standard form equation:
[tex]\[
(x - 13)^2 + (y - (-8))^2 = 7^2
\][/tex]
3. Simplify the equation:
Since subtracting a negative number is the same as adding the positive value:
[tex]\[
(x - 13)^2 + (y + 8)^2 = 49
\][/tex]
Thus, the equation of the circle in standard form is:
[tex]\[
(x - 13)^2 + (y + 8)^2 = 49
\][/tex]
