Question

question 21
find the equation in standard form of the circle graphed below.
question help: written example

Explanation:

Step1: Identify the center

The center of the circle is at the origin $(0,0)$ as it is centered on the intersection of the $x -$ and $y -$ axes.

Step2: Determine the radius

The circle intersects the $x -$ axis at $x = 3$ and $x=- 3$. The radius $r$ is the distance from the center $(0,0)$ to a point on the circle, so $r = 3$.

Step3: Write the standard - form equation

The standard - form equation of a circle is $(x - h)^2+(y - k)^2=r^2$, where $(h,k)$ is the center and $r$ is the radius. Substituting $h = 0$, $k = 0$, and $r = 3$ into the equation, we get $(x - 0)^2+(y - 0)^2=3^2$, which simplifies to $x^{2}+y^{2}=9$.

Answer:

$x^{2}+y^{2}=9$