Circles Objectives: Write an equation for a circle given sufficient information Given an equation of a circle, graph it and label the radius and the center

Standard Equation of a Circle OP = r P(x,y) r O

Standard Equation of a Circle An equation for the circle with its center at (0,0) and a radius of r is

Example 1 Write the standard equation of the circle whose center is at the origin and whose radius is 4. Sketch the graph. -4 -2 2 4

Standard Equation of a Circle The standard equation for a translated circle is (x – h)2 + (y – k)2 = r2 center: (h, k) radius: r

Example 2 Write the standard equation of the circle graphed below. -6 -8 6 8 2 4 -4 -2

Practice Write the standard equation of a circle with the following center and radius. 1) C(0,0) radius: 9 2) C(2,3) radius: 5 3) C(-5,2) radius: 4

Practice Graph each equation. Label the center and radius. 1) x2 + y2 = 25 Center = (0, 0) radius = 5 2) (x – 2)2 + y2 = 4 Center = (2, 0) radius = 2 3) (x + 4)2 + (y – 3)2 = 49 Center = (-4, 3) radius = 7

Example 3 Write the standard equation for the circle given by x2 + y2 – 12x – 2y - 8 = 0. State the coordinates of its center and give its radius. Center: (6,1) Radius:

Example 4 Write the standard equation for the circle given by x2 + y2 + 6x – 4y - 3 = 0. State the coordinates of its center and give its radius. Then sketch the graph. -6 -8 6 8 2 4 -4 -2 Center: (-3,2) Radius:

Practice Write the standard equation for the circle given by x2 + y2 - 2x + 2y - 7 = 0. State the coordinates of its center and give its radius. Then sketch the graph. Center = (1, 1) Radius = 3