Question

1. - / 2 points find the center and the radius r of the circle given by the following equation. (x + 5)^2+(y - 6)^2 = 49 center (x, y) = ( ) radius r = units resources master it

Explanation:

Step1: Recall circle - equation form

The standard form of a circle's 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 $(x + 5)^2+(y - 6)^2 = 49$, we have $x+5=x-(-5)$ and $y - 6$. So the center $(x,y)=(-5,6)$.

Step3: Identify the radius

Since $r^2 = 49$, taking the square - root of both sides (and considering the non - negative value for the radius), we get $r=\sqrt{49}=7$.

Answer:

center $(x,y)=(-5,6)$
radius $r = 7$ units