1. Circles

2. Equation of a circle: ( x – h )2 )2 + ( y – k )2 )2 = r2r2 Center of the circle: C( h, k ) Radius of the circle: r Diameter of the circle: d = 2r rr d= 2r Example 5: Find the center and the radius of a circle whose equation is ( x – 3) 2 + ( y + 5 )2 )2 = 36. Solution: Center: C( 3, -5) Radius: r = 6 Example 6: Graph the above Circle. 6 6 6 6 (3,-5) (9, -5)(-3, -5) (3, -11) (3, 1 ) x y

3. Graphing Semi Circles Upper half, Lower half, right half, and left half Let us find the equations of the upper half, lower half, right half and left half of the circle x2 x2 + y2 y2 = 25. x2 x2 + y2 y2 = 25 is a circle with center ( 0, 0 ) and radius r = 5. The graph of this circle is shown below. To find upper and lower halves, we solve for y in terms of x. 1) Represents the upper half plane -5 5 5 5 5 0 5

4. Continued … To find right and left halves, we solve for x in terms of y. -5 5 5 3) Represents the right half plane 4) Represents the left half plane

5. The End