Question

the equation of a circle is given below. identify the radius and center. then graph the
$(x - 3)^2+(y + 2)^2 = 25$
radius:
center: ( )

Explanation:

Step1: Recall the standard form of a circle's 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 the center

For the equation \((x - 3)^2+(y+2)^2 = 25\), we can rewrite \(y + 2\) as \(y-(-2)\). Comparing with \((x - h)^2+(y - k)^2=r^2\), we have \(h = 3\) and \(k=-2\). So the center \((h,k)=(3,-2)\).

Step3: Identify the radius

Since \(r^2 = 25\), taking the square - root of both sides (and considering \(r>0\) as radius is a non - negative quantity), we get \(r=\sqrt{25}=5\).

Answer:

Radius: \(5\)
Center: \((3,-2)\)