Math Problem Statement
Consider the following equation of a circle.
(x+6)2+(y+6)2=4
Step 3 of 3 : Graph the circle.
Solution
The equation you provided is in the standard form of a circle's equation:
Where:
- is the center of the circle
- is the radius of the circle
In your equation:
We can rewrite it as:
So, the center is , and the radius is:
Graphing the Circle:
-
Center: The center of the circle is at the point .
-
Radius: The radius of the circle is 2 units.
-
Points on the Circle: To graph the circle, we can plot several key points:
- Move 2 units to the right of the center:
- Move 2 units to the left of the center:
- Move 2 units up from the center:
- Move 2 units down from the center:
-
Draw the Circle: After plotting these points, sketch the circle, making sure it is centered at 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:
- What happens to the graph if the center of the circle is shifted to another point?
- How does the radius affect the size of the circle on the graph?
- How would the equation change if the radius were doubled?
- What is the relationship between the circle’s radius and its area?
- How does this circle compare to one with the equation ?
Tip:
Remember that the general form of a circle's equation, , is a very handy tool for quickly identifying the center and radius of a circle in any given equation.
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Math Problem Analysis
Mathematical Concepts
Geometry
Equations of Circles
Formulas
(x - h)² + (y - k)² = r²
Theorems
Standard Equation of a Circle
Suitable Grade Level
Grades 9-11