Question

find the center and radius of the circle represented by the equation below.
$(x + 12)^2 + (y - 7)^2 = 196$
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 \(h\) and \(k\) from the given equation

Given \((x + 12)^2 + (y - 7)^2 = 196\), rewrite \(x + 12\) as \(x - (-12)\). So, \(h = -12\) and \(k = 7\).

Step3: Find the radius \(r\)

Since \(r^2 = 196\), take the square root of both sides: \(r = \sqrt{196} = 14\).

Answer:

Center: \((-12, 7)\)
Radius: \(14\)