Question

find the center and radius of the circle represented by the equation below.
$(x + 7)^2 + (y - 6)^2 = 361$
answer attempt 1 out of 2
center: ( , )

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 \(h\) and \(k\) from the given equation

Given \((x + 7)^2 + (y - 6)^2 = 361\), we can rewrite \(x + 7\) as \(x - (-7)\). So comparing with the standard form, \(h = -7\) and \(k = 6\).

Step3: Find the radius

Since \(r^2 = 361\), we take the square root of both sides. \(r=\sqrt{361}=19\) (we take the positive root as radius is non - negative).

Answer:

Center: \((-7, 6)\)
Radius: \(19\)