Write and Graph Equations of Circles Chapter 10: Circles

Equations of a circle In an xy plane a circle is defined by: x 2 + y 2 = r 2 where r is the radius of the circle (x, y) (x, 0) (0, y)

Why is it backwards? For a circle with radius r centered at (h, k) the equation is written: (x - h) 2 + (y - k) 2 = r 2 (1, 1) (x - 1) 2 + (y - 1) 2 = 1 h = 1 k = 1 r = 1 (1, 1)  center

Write the equation in standard form (x + 1) 2 + (y - 2) 2 = 4 (x – (-1)) 2 + (y – (2)) 2 = 2 2 (x – h) 2 + (y – k) 2 = r 2

Identify the special line or line segment Circle: (x + 3) 2 + (y - 6) 2 = 25 Line: Diameter Center  (-3, 6) r = 5

Homework p , 2, 5 – 8, 11 – 14, 16, 31 – 35, 49 – 54 report your answer in terms of  do not use  = 3.14 except to check answers