Question

graph the circle.
$x^{2}+y^{2}=81$

Explanation:

Step1: Recall circle - equation form

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 $(x - 0)^2+(y - 0)^2 = 9^2$. So the center of the circle is at the origin $(0,0)$ and the radius $r = 9$.

Step2: Identify key - points

We can find the points where the circle intersects the $x$ - axis and $y$ - axis. When $y = 0$, we have $x^{2}=81$, so $x=\pm9$. When $x = 0$, we have $y^{2}=81$, so $y=\pm9$. The circle intersects the $x$ - axis at $(-9,0)$ and $(9,0)$, and the $y$ - axis at $(0, - 9)$ and $(0,9)$.

Step3: Sketch the circle

Using the center $(0,0)$ and radius $r = 9$ and the key - points $(-9,0),(9,0),(0, - 9),(0,9)$, we can draw a smooth circular curve on the grid.

Answer:

Sketch a circle centered at the origin $(0,0)$ with a radius of 9, passing through the points $(-9,0),(9,0),(0, - 9),(0,9)$.