Question

find the center and radius of the circle defined by the equation (x + 5)^2+(y + 8)^2 = 25. center: ( , ) radius:

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

For the equation $(x + 5)^2+(y + 8)^2 = 25$, we have $x+5=x-(-5)$ and $y + 8=y-(-8)$. So the center is $(-5,-8)$.

Step3: Identify the radius

Since $r^2 = 25$, then $r=\sqrt{25}=5$.

Answer:

center: $(-5,-8)$
radius: $5$