Question

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

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

Since \(r^2=4^2\), then \(r = 4\) (radius is non - negative).

Answer:

4 units