To find the center and radius of the circle from the given equation:
[tex]\[ (x - 5)^2 + (y - 1)^2 = 30 \][/tex]
we should compare it to the standard form of the equation of a circle:
[tex]\[ (x - h)^2 + (y - k)^2 = r^2 \][/tex]
Here, [tex]\( h \)[/tex] and [tex]\( k \)[/tex] are the coordinates of the center, and [tex]\( r \)[/tex] is the radius.
1. Identify the center [tex]\((h, k)\)[/tex]:
- From the equation [tex]\((x - h)^2 + (y - k)^2 = r^2\)[/tex], we see that [tex]\(h = 5\)[/tex] and [tex]\(k = 1\)[/tex]. Therefore, the center of the circle is [tex]\((5, 1)\)[/tex].
2. Identify the radius [tex]\(r\)[/tex]:
- From the equation [tex]\((x - 5)^2 + (y - 1)^2 = 30\)[/tex], we see that [tex]\(r^2 = 30\)[/tex]. To find the radius [tex]\(r\)[/tex], we take the square root of 30.
- Thus, [tex]\(r = \sqrt{30}\)[/tex].
Therefore, the correct answer is:
Center: [tex]\((5, 1)\)[/tex], Radius: [tex]\(\sqrt{30}\)[/tex]
