8.1 The Rectangular Coordinate System and Circles Part 2: Circles.

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Presentation transcript:

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 = r 2. If the center is at the origin, the equation is x 2 + y 2 = r 2.

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 x 2 + y 2 + 2x + 6y – 15 = 0.

 Find the center and radius for the circle whose equation is x 2 + y 2 – 8x – 12y + 3 = 0.