10.7.1 Write and Graph Equations of Circles

Chapter 10: Circles

Equations of a circleIn an xy plane a circle is defined by:x2 + y2 = r2

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 = r2

(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 = 22

(x – h)2 + (y – k)2 = r2

Identify the special line or line segment

Circle: (x + 3)2 + (y - 6)2 = 25Line:

234

xy

Diameter

Center (-3, 6)r = 5

Homeworkp. 702 1, 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