Consider the following equation of a circle.

(x+6)2+(y+6)2=4

Step 3 of 3 :  Graph the circle.


The equation you provided is in the standard form of a circle's equation:

\[
(x - h)^2 + (y - k)^2 = r^2
\]

Where:
- \((h, k)\) is the center of the circle
- \(r\) is the radius of the circle

In your equation:

\[
(x + 6)^2 + (y + 6)^2 = 4
\]

We can rewrite it as:

\[
(x - (-6))^2 + (y - (-6))^2 = 4
\]

So, the center \((h, k)\) is \((-6, -6)\), and the radius \(r\) is:

\[
r = \sqrt{4} = 2
\]

### Graphing the Circle:

1. **Center**: The center of the circle is at the point \((-6, -6)\).
2. **Radius**: The radius of the circle is 2 units.
3. **Points on the Circle**: To graph the circle, we can plot several key points:
   - Move 2 units to the right of the center: \((-6 + 2, -6) = (-4, -6)\)
   - Move 2 units to the left of the center: \((-6 - 2, -6) = (-8, -6)\)
   - Move 2 units up from the center: \((-6, -6 + 2) = (-6, -4)\)
   - Move 2 units down from the center: \((-6, -6 - 2) = (-6, -8)\)

4. **Draw the Circle**: After plotting these points, sketch the circle, making sure it is centered at \((-6, -6)\) and has a radius of 2 units.

Would you like me to generate a visual graph of this circle, or provide further details on how to plot it? Let me know!

### Relative Questions:
1. What happens to the graph if the center of the circle is shifted to another point?
2. How does the radius affect the size of the circle on the graph?
3. How would the equation change if the radius were doubled?
4. What is the relationship between the circle’s radius and its area?
5. How does this circle compare to one with the equation \((x - 3)^2 + (y - 4)^2 = 16\)?

### Tip:
Remember that the general form of a circle's equation, \((x - h)^2 + (y - k)^2 = r^2\), is a very handy tool for quickly identifying the center and radius of a circle in any given equation.

Consider the following equation of a circle: (x+6)²+(y+6)²=4. Step 3 of 3: Graph the circle.

Learn how to graph the circle represented by the equation (x+6)² + (y+6)² = 4. This problem involves identifying the center and radius of the circle and plotting key points. Perfect for students in Grades 9-11 studying geometry and the equation of circles.

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