Question

find the radius of the circle.
$(x - 3)^2 + (y + 7)^2 = 16$
radius = ?

Explanation:

Step1: Recall circle equation form

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 given equation

Given equation: \((x - 3)^2 + (y + 7)^2 = 16\). Rewrite \(16\) as \(4^2\), so the equation becomes \((x - 3)^2 + (y + 7)^2 = 4^2\).

Step3: Identify radius

Comparing with standard form, \(r^2 = 16\) (or \(r^2 = 4^2\)), so \(r = 4\) (radius is positive).

Answer:

4