Equation of a Circle

What is the center of a circle whose equation is x2 + y2 - 12x - 2y + 12 = 0?

(6, 1)

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

(−9,6)

Which equation represents a circle with the same radius as the circle shown but with a center at (-1, 1)?

(x + 1)2 + (y - 1)2 = 16

Which equation represents a circle that contains the point (-5, -3) and has a center at (-2, 1)?

(x + 2)2 + (y - 1)2 = 25

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

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

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

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

(-2, 4)

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

(2, √ ̅21)

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

2 units

Does the point (2,root of 6) lie on the circle shown? Explain.

No, the distance from (0, 0) to (2, root of 6) is not 3 units.

Which explains how to find the radius of a circle whose equation is in the form x2 + y2 = z?

The radius is the square root of the constant term, z.

Does the point (1, StartRoot 7 EndRoot) lie on the circle shown? Explain.

Yes, the distance from (-2, 0) to (1, ) is 4 units.

Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options.

x2 + (y - 3)2 = 36 x2 + (y + 8)2 = 36