Question

find the center and the radius r of the circle with the following equation. x^2 + y^2 = 49 center (x, y) = ( ) radius r = units resources master it

Explanation:

Step1: Recall circle - equation form

The standard form of the equation of a circle is $(x - a)^2+(y - b)^2=r^2$, where $(a,b)$ is the center of the circle and $r$ is the radius.
The given equation is $x^{2}+y^{2}=49$, which can be written as $(x - 0)^2+(y - 0)^2 = 7^2$.

Step2: Identify the center

Comparing with the standard form, when $a = 0$ and $b = 0$, the center of the circle $(x,y)=(0,0)$.

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 $r = 7$.

Answer:

center $(x,y)=(0,0)$
radius $r = 7$ units