Question

find the center and radius of the circle represented by the equation below.
$(x + 3)^2 + (y - 9)^2 = 25$
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 \(h\), \(k\), and \(r\) from the given equation

Given \((x + 3)^2 + (y - 9)^2 = 25\), we can rewrite \(x + 3\) as \(x - (-3)\). So comparing with the standard form, \(h = -3\), \(k = 9\), and \(r^2 = 25\).

Step3: Find the radius

To find \(r\), we take the square root of \(r^2\). Since \(r^2 = 25\), then \(r=\sqrt{25}=5\) (we take the positive root as radius is a length).

Answer:

Center: \((-3, 9)\)
Radius: \(5\)