Question

find the center and radius of the circle represented by the equation below.
$(x - 13)^2 + (y + 11)^2 = 361$
answer attempt 1 out of 2
center: (□,□)
radius: □

Explanation:

Step1: Recall the standard circle equation

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

Step2: Identify \(h\), \(k\), and \(r\) from the given equation

For the equation \((x - 13)^2 + (y + 11)^2 = 361\), we can rewrite \(y + 11\) as \(y - (-11)\). So comparing with \((x - h)^2 + (y - k)^2 = r^2\), we have \(h = 13\), \(k = -11\), and \(r^2 = 361\).

Step3: Calculate the radius

To find \(r\), we take the square root of \(r^2\). Since \(r^2 = 361\), then \(r=\sqrt{361}=19\).

Answer:

Center: \((13, -11)\)
Radius: \(19\)