Algebra II - Graphing Circular Inequalities

$(x-1)^2+(y-1)^2\geq25$

Given the above circle inequality, which point is not on the edge of the circle?

Explanation

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.

$(x-1)^2+(y-1)^2\geq25$

Given the above circle inequality, which point satisfies the inequality?

Explanation

The left side of the equation must be greater than or equal to 25 in order to satisfy the equation, so plugging in each of the values for x and y, we see that:

$(7-1)^2+(4-1)^2= 6^2+3^2=36+9\geq25$

$(5-1)^2+(2-1)^2= 4^2+1^2=16+1\leq25$

$(0-1)^2+(0-1)^2= 1^2+1^2=1+1\leq25$

$(3-1)^2+(3-1)^2= 2^2+2^2=4+4\leq25$

The only point that satisfies the inequality is (7,4) since it yields an answer that is greater than or equal to 25.

$(x-1)^2+(y-1)^2\geq25$

Given the above circle inequality, does the center satisfy the equation?

Yes

Can't tell

Maybe

Explanation

The center of the circle is , so plugging those values in for x and y yields the response that 0 is greater than or equal to 25.

Since plugging in the center values gives us a false statement we know that our center does not satisfy the inequality.

$(x-1)^2+(y-1)^2\geq25$

Given the above circle inequality, is the shading on the graph inside or outside the circle?

Outside

Inside

Can't Tell

Both

Explanation

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.

$(x+2)^2+(y-4)^2\geq36$

Given the above circle inequality, which point is not on the edge of the circle?

Explanation

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.

$(x+2)^2+(y-4)^2\geq36$

Given the above circle inequality, which point satisfies the inequality?

Explanation

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:

$(0+2)^2+(10-4)^2=2^2+6^2=4+36\geq36$

$(3+2)^2+(4-4)^2=5^2+0^2=25\leq36$

$(0+2)^2+(0-4)^2=2^2+4^2=4+16\leq36$

$(-2+2)^2+(4-4)^2=0^2+0^2=0\leq36$

Therefore only yields an answer that is greater than or equal to 36.

$(x+2)^2+(y-4)^2\geq36$

Given the above circle inequality, does the center satisfy the equation?

Yes

Can't tell

Maybe

Explanation

$(x+2)^2+(y-4)^2\geq36$

The center of the circle is , so plugging those values in for x and y yields the response,

Therefore, the center does not satisfy the inequality.

$(x+2)^2+(y-4)^2\geq36$

Given the above circle inequality, is the shading on the graph inside or outside the circle?

Outside

Inside

Can't tell

Both

Explanation

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.

Which equation would match to this graph:

Circle inequality 1