Question

the equation for the circle below is $x^{2}+y^{2}=81$. what is the length of the circles radius? a. 16 b. 2 c. 81 d. -1 e. 9 f. 4

Explanation:

Step1: Recall circle - equation formula

The standard form of the equation of a circle centered at the origin $(0,0)$ is $x^{2}+y^{2}=r^{2}$, where $r$ is the radius.

Step2: Compare given equation with standard form

Given $x^{2}+y^{2}=81$, and since $x^{2}+y^{2}=r^{2}$, we have $r^{2}=81$.

Step3: Solve for $r$

Taking the square - root of both sides, $r=\sqrt{81}$. Since $r$ represents the radius (a non - negative quantity), $r = 9$.

Answer:

E. 9