Algebra II : Graphing Circular Inequalities
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Example Questions
Example Question #1 : Graphing Circular Inequalities
Find an inequality for points on a graph that fall on or inside of a circle centered at 
The equation for a circle centered at point 
Example Question #1 : Graphing Circular Inequalities
Given the above circle inequality, which point is not on the edge of the circle?
This is a graph of a circle with radius of 5 and a center of (1,1). The center of the circle is not on the edge of the circle, so that is the correct answer. All other points are exactly 5 units away from the circle's center, making them a part of the circle.
Example Question #2 : Graphing Circular Inequalities
Given the above circle inequality, does the center satisfy the equation?
Can't tell
Yes
No
Maybe
No
The center of the circle is 
Since plugging in the center values gives us a false statement we know that our center does not satisfy the inequality.
Example Question #1 : Graphing Circular Inequalities
Given the above circle inequality, is the shading on the graph inside or outside the circle?
Can't Tell
Inside
Outside
Both
Outside
Check the center of the circle to see if that point satisfies the inequality.
When evaluating the function at the center (1,1), we see that it does not satisfy the equation, so it cannot be in the shaded region of the graph.
Therefore the shading is outside of the circle.
Example Question #1 : Graphing Circular Inequalities
Given the above circle inequality, which point is not on the edge of the circle?
This is a graph of a circle with radius of 6 and a center of (-2,4). The point (2,2) is not on the edge of the circle, so that is the correct answer. All other points are exactly 6 units away from the circle's center, making them a part of the circle.
Example Question #1 : Graphing Circular Inequalities
Given the above circle inequality, which point satisfies the inequality?
The left side of the equation must be greater than or equal to 36 in order to satisfy the equation, so plugging in each of the values for x and y, we see:
Therefore only 
Example Question #1 : Graphing Circular Inequalities
Given the above circle inequality, does the center satisfy the equation?
Can't tell
No
Maybe
Yes
No
The center of the circle is 
Therefore, the center does not satisfy the inequality.
Example Question #2 : Graphing Circular Inequalities
Given the above circle inequality, is the shading on the graph inside or outside the circle?
Outside
Inside
Both
Can't tell
Outside
Check the center of the circle to see if that point satisfies the inequality. When evaluating the function at the center (-2,4), we see that it does not satisfy the equation, so it cannot be in the shaded region of the graph. Therefore the shading is outside of the circle.
Example Question #2 : Graphing Circular Inequalities
Given the above circle inequality, which point is not on the edge of the circle?
Recall the equation of a circle:
This is a graph of a circle with radius of 2 and a center of (-4,-3). The point (2,3) is not on the edge of the circle, so that is the correct answer.
All other points are exactly 2 units away from the circle's center, making them a part of the circle's edge.
Example Question #1 : Graphing Circular Inequalities
Given the above circle inequality, which point satisfies the inequality?
The left side of the equation must be less than or equal to 4 in order to satisfy the equation, so plugging in each of the values for x and y, we see:
The only point that satisfies the inequality is the point (-3,-2), since it yields an answer that is less than or equal to 4.
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