Question

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

Explanation:

Step1: Recall circle - equation formula

The standard form of a circle's equation is $(x - a)^2+(y - b)^2=r^2$, where $(a,b)$ is the center of the circle and $r$ is the radius.

Step2: Compare given equation with standard form

Given $(x - 3)^2+(y + 7)^2 = 16$, we can rewrite $16$ as $4^2$. So, $r^2=16$.

Step3: Solve for the radius

Taking the square - root of both sides of $r^2 = 16$, we get $r = 4$ (we take the positive value since the radius is a non - negative quantity).

Answer:

$4$