8.1 The Rectangular Coordinate System and Circles

Part 2: Circles

Circles

• An application of the distance formula leads to one of the most familiar shapes in geometry, the circle.

• A circle is the set of all points in a plane that lie a fixed distance from a fixed point.

• The fixed point is called the center and the fixed distance is called the radius.

Equation of a Circle

• The equation of a circle of radius r with center at (h, k) is (x – h)2 + (y – k)2 = r2.

• If the center is at the origin, the equation isx2 + y2 = r2.

Finding an Equation of a Circle

• Find an equation of a circle with center at (-1, 2) and radius 4.

Find an equation of a circle with center at (2, -2) and radius 3.

Finding an Equation of a Circle and Graphing

• Find an equation of the circle with radius 3 and center at (0, 0), and graph the circle.

Find an equation of the circle with center at (4, -3) and radius 5, and graph the circle.

Completing the Square

• Find the center and radius for the circle whose equation is x2 + y2 + 2x + 6y – 15 = 0.

Find the center and radius for the circle whose equation is x2 + y2 – 8x – 12y + 3 = 0.