Question

consider the following equation of a circle.

$x^{2}+y^{2}+6x - 6y-18 = 0$

step 3 of 3: graph the circle.

answer 2 points

press the plot button to add the graph to the grid. points can be moved by dragging or using the arrow keys. points whose positions are related to a moved point will be updated automatically. any curves will update whenever a point is moved.

Explanation:

Step1: Rewrite the equation in standard form.

Complete the square for \(x\) and \(y\) terms.
\[

$$\begin{align*} x^{2}+y^{2}+6x - 6y-18&=0\\ x^{2}+6x + y^{2}-6y&=18\\ x^{2}+6x + 9+y^{2}-6y+9&=18 + 9+9\\ (x + 3)^{2}+(y - 3)^{2}&=36 \end{align*}$$

\]

Step2: Identify the center and radius.

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 \((x + 3)^{2}+(y - 3)^{2}=36\), the center is \((-3,3)\) and the radius \(r = 6\).

Step3: Graph the circle.

Plot the center \((-3,3)\) on the coordinate plane. Then, from the center, move 6 units in all directions (up, down, left, right) to get points on the circle. Connect these points to form a circle.

Answer:

Graph a circle with center \((-3,3)\) and radius \(6\) on the given coordinate - plane.