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

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. 

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.

Recall the equation of a circle:

 where r is the radius and (h,k) is the center of the 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.

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.

Recall the equation of circle:

 where r is the radius and the center of the circle is at (h,k).

The center of the circle is (-4,-3), so plugging those values in for x and y yields the response that 0 is less than or equal to 4, which is a true statement, so the center does satisfy the inequality. 

Check the center of the circle to see if that point satisfies the inequality. When evaluating the function at the center (-4,-3), we see that it does satisfy the equation, so it can be in the shaded region of the graph. Therefore the shading is inside of the circle.

The -intercepts of a function are the points where . When we substitute this into our equation, we get: 

. 

Adding nine to both sides, 

. 

Modifying the equation to get like bases get us,

Since .

Now we can set the exponents equal to eachother and solve for .

Thus, 

. 

Giving us our final solution: 

. 

The general equation of a circle is where the center is and the radius is .

In this case, the center is and the radius is , so the equation for this circle is .

The circle is shaded on the inside, which means that choosing any point  and plugging it in for would produce something less than .

Therefore, our answer is .

The general equation for a circle is where the center is and its radius is .

In this case, the center is  and the radius is , so the equation for the circle is .

We can simplify this equation to: .

The circle is shaded on the inside, which means that choosing any point and plugging it in for  would produce something less than . 

Therefore, our answer is .