Question

a circle has an equation of (x - 5)^2+(y - 1)^2 = 30. what is the center and radius of the circle? select the correct answer. center: (5,1), radius: √30 center: (-5,-1), radius: √30 center: (5,1), radius: 30 center: (-5,-1), radius: 30

Explanation:

Step1: Recall circle - equation formula

The standard form of the equation of a circle is \((x - h)^2+(y - k)^2=r^2\), where \((h,k)\) is the center of the circle and \(r\) is the radius.

Step2: Identify the center

Given the equation \((x - 5)^2+(y - 1)^2 = 30\), by comparing with the standard - form \((x - h)^2+(y - k)^2=r^2\), we can see that \(h = 5\) and \(k = 1\), so the center of the circle is \((5,1)\).

Step3: Identify the radius

Since \(r^2=30\), then \(r=\sqrt{30}\).

Answer:

Center: \((5,1)\), Radius: \(\sqrt{30}\)