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: (\boxed{}, \boxed{})

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

Answer:

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