graph the circle x² + y² = 81. plot the center. then plot a point on the circle. if you make a mistake, you…

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 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 is $(0,0)$ and the radius $r = 9$.

Step2: Plot the center

Plot the point $(0,0)$ on the coordinate - plane.

Step3: Plot a point on the circle

We can find a point on the circle by using the radius. For example, when $x = 9$ and $y = 0$ (since $x^{2}+y^{2}=81$, substituting $x = 9$ gives $9^{2}+0^{2}=81$). Plot the point $(9,0)$ on the circle.

To graph the full circle, we can find other points by symmetry. The circle is symmetric about the $x$ - axis, $y$ - axis, and the origin.

Answer:

Center: $(0,0)$; A point on the circle: $(9,0)$ (There are many other possible points on the circle such as $(0,9),(- 9,0),(0, - 9)$ etc.)