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.

The equation for a horizontal hyperbola is. The equation for a vertical hyperbola is . Hyperbolic inequalities use an inequality sign rather than an equals sign, but otherwise have the same form as hyperbolic equations. The fact that the right side of the inequality is not equal to 1 does not change the fact that , and represent hyperbolas, since THESE can all be simplified to create an inequality with 1 on the right side (by dividing both sides of the equation by the constant on the right side of the inequality.) Answer choice is the only option in which the two terms on the left side of the inequality are combined using addition rather than subtraction, creating an ellipse rather than a hyperbola. (The equation for an ellipse is .)

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.

The hyperbola in the question's graph is .

This could be discerned because it subtracts from and not the other way around, putting the zeros on the axis. This narrows the answers down to and .

Test a point to tell which inequality is being used in the graph.

The point is within the shaded region, for example.

, which is greater than 16, so the answer is .

The equation for a horizontal hyperbola is. The equation for a vertical hyperbola is . Hyperbolic inequalities use an inequality sign rather than an equals sign, but otherwise have the same form as hyperbolic equations. The fact that the right side of the inequality is not equal to 1 does not change the fact that , and represent hyperbolas, since THESE can all be simplified to create an inequality with 1 on the right side (by dividing both sides of the equation by the constant on the right side of the inequality.) Answer choice is the only option in which the two terms on the left side of the inequality are combined using addition rather than subtraction, creating an ellipse rather than a hyperbola. (The equation for an ellipse is .)

The hyperbola in the question's graph is .

This could be discerned because it subtracts from and not the other way around, putting the zeros on the axis. This narrows the answers down to and .

Test a point to tell which inequality is being used in the graph.

The point is within the shaded region, for example.

, which is greater than 16, so the answer is .

The equation for a horizontal hyperbola is . The equation for a vertical hyperbola is . Hyperbolic inequalities use an inequality sign rather than an equals sign, but otherwise have the same form as hyperbolic equations. The presence of coefficients in and does not change the fact that and represent hyperbolas, since both can be simplified to remove those coefficients (by dividing the numerator and denominator of terms with coefficients by those coefficients.) Answer choice is missing an exponent of 2 on the first term in the inequality, and therefore does not match the form of a hyperbola.

The equation for a horizontal hyperbola is . The equation for a vertical hyperbola is . Hyperbolic inequalities use an inequality sign rather than an equals sign, but otherwise have the same form as hyperbolic equations. The presence of coefficients in and does not change the fact that and represent hyperbolas, since both can be simplified to remove those coefficients (by dividing the numerator and denominator of terms with coefficients by those coefficients.) Answer choice is missing an exponent of 2 on the first term in the inequality, and therefore does not match the form of a hyperbola.

The hyperbola in the graph has y-intercepts rather than x-intercepts, so the equation must be in the form and not the other way around.

The y-intercepts are at 1 and -1, so the correct equation will have just and not .

The answer not must either be,

or .

To see which, test a point in the shaded area.

For example, .

, which is less than 1, so the answer is .

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:

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