Equation of a Circle

What is the center of a circle whose equation is x2 + y2 + 4x - 8y + 11 = 0?

(-2,4)

The center of a circle represented by the equation (x + 9)2 + (y − 6)2 = 102 is

(-9,6)

What is the radius of a circle whose equation is x2 + y2 + 8x - 6y + 21 = 0?

2

Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Check all that apply.

x^{2}+(y-3)^{2}=36 x^{2}+(y+8)^{2}=36

Which equation represents a circle with a center at (-3, -5) and a radius of 6 units?

(x + 3)² + (y + 5)² = 36

Which equation represents a circle with a center at (-4, 9) and a diameter of 10 units?

(x + 4)2 + (y - 9)2 = 25

Which equation represents a circle with the same center as the circle shown but with a radius of 2 units?

(x - 4)2 + (y - 5)2 = 4

Which equation represents a circle that contains the point (-2, 8) and has a center at (4, 0)?

(x - 4)2 + y2 = 100

Which point is on the circle centered at the origin with a radius of 5 units?

(2, √ ̅21)

In the diagram, a circle centered at the origin, a right triangle, and the Pythagorean theorem are used to derive the equation of a circle, x2 + y2 = r2. If the center of the circle were moved from the origin to the point (h, k) and point P at (x, y) remains on the edge of the circle, which could represent the equation of the new circle?

(x - h)2 + (y - k)2 = r2