graph the circle x² + y² = 16. plot the center. then plot a point on the circle. if you make a mistake, you…

Explanation:

Step1: Recall circle - standard form

The standard form of a circle is $(x - a)^2+(y - b)^2=r^2$, where $(a,b)$ is the center and $r$ is the radius. For the equation $x^{2}+y^{2}=16$, we can rewrite it as $(x - 0)^2+(y - 0)^2 = 4^2$. So the center of the circle is $(0,0)$ and the radius $r = 4$.

Step2: Plot the center

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

Step3: Plot points on the circle

We can find points on the circle by using the radius. When $x = 0$, then $y=\pm4$ (since $0^{2}+y^{2}=16$, so $y=\pm4$). When $y = 0$, then $x=\pm4$ (since $x^{2}+0^{2}=16$, so $x=\pm4$). Plot the points $(0,4)$, $(0, - 4)$, $(4,0)$ and $(-4,0)$ and then draw a smooth circle passing through these points.

Answer:

Plot the center at the origin $(0,0)$ and points $(4,0)$, $(-4,0)$, $(0,4)$, $(0, - 4)$ and draw a circle through them.