Question

give the center and radius of the circle described by the equation and graph the equation. use the graph to identify the relations domain and range. x² + y² = 81 what is the center of the circle? the circle is centered at the point (0,0). (type an ordered pair.) what is the radius of the circle? the radius of the circle is . (type an integer or a fraction.)

Explanation:

Step1: Recall the standard circle - equation

The standard form of a circle equation is $(x - a)^2+(y - b)^2=r^2$, where $(a,b)$ is the center of the circle and $r$ is the radius. For the equation $x^{2}+y^{2}=81$, we can rewrite it as $(x - 0)^2+(y - 0)^2 = 9^2$.

Step2: Determine the radius

Comparing $(x - 0)^2+(y - 0)^2 = 9^2$ with the standard - form $(x - a)^2+(y - b)^2=r^2$, we can see that $r^{2}=81$. Taking the square root of both sides, and since $r>0$, we have $r = 9$.

Answer:

9