Question

find the center and radius of the circle represented by the equation below.
$(x - 8)^2 + (y + 13)^2 = 361$
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 \((x - 8)^2 + (y + 13)^2 = 361\), we can rewrite \(y + 13\) as \(y - (-13)\). Comparing with the standard form:

• \(h = 8\) (from \(x - 8\))
• \(k = -13\) (from \(y - (-13)\))
• \(r^2 = 361\), so we take the square root of 361 to find \(r\). \(\sqrt{361}=19\), so \(r = 19\).

Answer:

Center: \((8, -13)\)
Radius: \(19\)