Question

find the center and radius of the circle represented by the equation below.
$(x + 5)^2 + (y - 1)^2 = 25$
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 the equation \((x + 5)^2 + (y - 1)^2 = 25\), we can rewrite \((x + 5)^2\) as \((x - (-5))^2\). So comparing with the standard form, \(h = -5\) and \(k = 1\).

Step3: Identify the radius \(r\)

From the equation \((x + 5)^2 + (y - 1)^2 = 25\), we know that \(r^2 = 25\). Taking the square root of both sides, \(r=\sqrt{25} = 5\) (we take the positive root since radius is a length).

Answer:

Center: \((-5, 1)\)
Radius: \(5\)