Question

find the center and radius of the circle represented by the equation below.
$(x + 11)^2 + (y - 10)^2 = 256$
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 \(r\) from the given equation

Given \((x + 11)^2 + (y - 10)^2 = 256\), we can rewrite \((x + 11)^2\) as \((x - (-11))^2\). So, comparing with the standard form, \(h = -11\), \(k = 10\), and \(r^2 = 256\).

Step3: Find the radius

To find \(r\), take the square root of \(r^2\). So, \(r = \sqrt{256} = 16\).

Answer:

Center: \((-11, 10)\)
Radius: \(16\)