Equation of a Circle

Which equation represents a circle with a center at (2, -8) and a radius of 11?

(x - 2)² + (y + 8)² = 121

A circle has a diameter of 12 units, and its center lies on the x-axis. What could be the equation of the circle? Check all that apply.

(x - 6)² + y² = 36 (x + 6)² + y² = 36

Concentric circles are circles with the same center but different radii. Which equations represent concentric circles along with the circle shown in the graph? Check all that apply.

(x - 8)² + (y - 9)² = 3 (x - 8)² + (y - 9)² = 14

The equation of a circle is x2 + (y - 10)2 = 16. The radius of the circle is units. The center of the circle is at .

4 (0, 10)

What is the radius of a circle given by the equation x2 + y2 - 2x + 8y - 47= 0? radius =

8 units

A circle centered at (-1, 2) has a diameter of 10 units. Amit wants to determine whether (2, -2) is also on the circle. His work is shown below. The radius is 5 units. Find the distance from the center to (2, -2). The point (2, -2) doesn't lie on the circle because the calculated distance should be the same as the radius. Is Amit's work correct?

No, he did not calculate the distance correctly.

Consider a circle whose equation is x2 + y2 + 4x - 6y - 36 = 0. Which statements are true? Check all that apply.

To complete the square for the x terms, add 4 to both sides. The center of the circle is at (-2, 3).

A circle centered at the origin contains the point (0, -9). Does (8, root of 17) also lie on the circle? Explain.

Yes, the distance from the origin to the point (8, root of 17) is 9 units.

To derive the standard formula of a circle, a radius r is constructed as the hypotenuse of a right triangle as shown. What are the lengths of the sides of the right triangle that is formed? Check all that apply.

x - h y - k

What is the equation of the circle shown in the graph?

x² + (y + 3)² = 4