Question

Find the center and radius of the circle, and sketch its graph.

$x^2+y^2=9$

Short answer

The center of the circle is (0, 0) and radius is 3 units. The graph of the circle is provided below.

Step-by-step solution

Step 1. Apply the concept of circles.

The standard form of the equation of the circle is ${\left(x-h\right)}^2+{\left(y-k\right)}^2=r^2$, where$\left(h,k\right)$ denote the center of the circle andr denote the radius.

Step 2. Interpret the values of center and radius.

Consider the provided equation.

$x^2+y^2=9$

Rewrite the equation as provided below.

${\left(x-0\right)}^2+{\left(y-0\right)}^2=3^2$

Recall that the standard form of the equation of the circle is ${\left(x-h\right)}^2+{\left(y-k\right)}^2=r^2$, where $\left(h,k\right)$ denote the center of the circle and r denote the radius.

Compare, $\left(h,k\right)$and $\left(0,0\right)$ also radius r is 3.

Here, $h=0,k=0\text{and}r=3$.

Therefore, the center of the circle is $\left(0,0\right)$ and the radius is 3 units.

Step 3. Graph the circle.

Now, on the Cartesian plane construct a circle with a center at origin and radius 3 units.

The graph obtained is provided below,

Thus, the center of the circle is (0, 0) and radius is 3 units.