Question

what is the radius of a circle whose equation is $(x + 5)^2+(y - 3)^2 = 4^2$?
2 units
4 units
8 units
16 units

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: Compare the given equation with the standard form

Given \((x + 5)^2+(y - 3)^2=4^2\), comparing with \((x - h)^2+(y - k)^2=r^2\), we can see that \(r^2 = 4^2\).

Step3: Find the radius \(r\)

Since \(r^2=4^2\), taking the square root of both sides (and considering \(r>0\) as radius is a non - negative quantity), we get \(r = 4\).

Answer:

4 units