Question

find the center and radius of the circle represented by the equation below.
$(x - 8)^2 + (y + 2)^2 = 324$
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

Given the equation \((x - 8)^2 + (y + 2)^2 = 324\), we can rewrite \(y + 2\) as \(y - (-2)\). So, comparing with the standard form:

• \(h = 8\) (from \(x - 8\))
• \(k = -2\) (from \(y - (-2)\))
• \(r^2 = 324\)

Step3: Find the radius \(r\)

To find \(r\), we take the square root of \(r^2\). So, \(r=\sqrt{324}=18\) (we take the positive square root since radius is a length).

Answer:

Center: \((8, -2)\)
Radius: \(18\)