To determine the center of the circle given by the equation [tex]\((x+7)^2 + (y-13)^2 = 196\)[/tex], we follow these steps:
1. The general form of the equation of a circle is [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.
2. Compare the given equation [tex]\((x+7)^2 + (y-13)^2 = 196\)[/tex] with the general form:
- [tex]\((x+7)^2\)[/tex] can be rewritten as [tex]\((x - (-7))^2\)[/tex]. This indicates that [tex]\(h = -7\)[/tex].
- [tex]\((y-13)^2\)[/tex] directly matches the form [tex]\((y - k)^2\)[/tex], indicating that [tex]\(k = 13\)[/tex].
3. Therefore, the center of the circle [tex]\((h, k)\)[/tex] is [tex]\((-7, 13)\)[/tex].
Final answer:
- The value for [tex]\(h\)[/tex] (the x-coordinate of the center) is [tex]\(-7\)[/tex].
- The value for [tex]\(k\)[/tex] (the y-coordinate of the center) is [tex]\(13\)[/tex].
So, the center of the circle is [tex]\((-7, 13)\)[/tex].
