Question

determine the center and radius of the circle.
$(x - 6)^2+(y - 7)^2 = 25$

Explanation:

Step1: Recall circle - equation form

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

Step2: Identify the center

Comparing $(x - 6)^2+(y - 7)^2=25$ with $(x - a)^2+(y - b)^2=r^2$, we have $a = 6$ and $b = 7$, so the center is $(6,7)$.

Step3: Identify the radius

Since $r^2=25$, taking the square - root of both sides (and considering the positive value for the radius), we get $r=\sqrt{25}=5$.

Answer:

Center: $(6,7)$; Radius: $5$