Question

find the center and radius of the circle represented by the equation below.
$(x - 14)^2 + (y + 3)^2 = 256$
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 \(r^2\) from the given equation

For the equation \((x - 14)^2 + (y + 3)^2 = 256\), we can rewrite \(y + 3\) as \(y - (-3)\). So comparing with the standard form:

• \(h = 14\) (from \(x - 14\))
• \(k = -3\) (from \(y - (-3)\))
• \(r^2 = 256\)

Step3: Find the radius \(r\)

To find \(r\), we take the square root of \(r^2\). So \(r=\sqrt{256}=16\) (we take the positive square root since radius is a length).

Answer:

Center: \((14, -3)\)
Radius: \(16\)