Question

find the center and radius of the circle having the given equation. $x^{2}+y^{2}=100$ radius: center: ()

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. The given equation $x^{2}+y^{2}=100$ can be written as $(x - 0)^2+(y - 0)^2 = 10^{2}$.

Step2: Identify center and radius

For the equation $(x - 0)^2+(y - 0)^2=10^{2}$, by comparing with the standard - form, the center $(a,b)=(0,0)$ and the radius $r = 10$.

Answer:

Radius: 10
Center: (0, 0)