CirclesLearning goals:

Write the equation of a circle. Use the equation of a circle and its

graph to solve problems. Graphing a circle using its four

quick points.

CIRCLES

What do you know about circles?

Definitions

Circle: The set of all points that are the same distance (equidistant) from a fixed point.

Center: the fixed points Radius: a segment whose

endpoints are the center and a point on the circle

RadiusCenter

The equation of circle centered at (0,0) and with radius r

x 2 + y 2 = r 2

Solution:Let P(x, y) represent

any point on the circle

1

0.5

-0.5

-1

-1.5

-2 -1 1 2

yx

PP

P

P

Finding the Equation of a Circle

The center is (0, 0) The radius is 12

The equation is: x 2 + y 2 = 144

Write out the equation for a circle centered at (0, 0) with radius =1

Solution:Let P(x, y) represent any point on the

circle

122 yx

Ex. 1: Writing a Standard Equation of a Circle centered at (0, 0) and radius 7.1

x 2 + y2 = r2 Standard equation of a circle.

x 2 + y2 = 7.12 = 50.41 Simplify.

Graphing Circles If you know the equation of a

circle, you can graph the circle by identifying its center and

radius; By listing four quick points: the

upmost, lowest, leftmost and rightmost points.

Graphing Circles Using 4 quick points

x 2 + y 2 = 9

Radius of 3Leftmost point (-3,0)Rightmost point(3,0)Highest point(0, 3)Lowest point(0, -3)

Is the point on, inside or outside of a circle x 2 + y 2 = 9?

)6,2(

)4,2(

)6,3(

Find the x and y intercepts algebraically.

2 2

4 4

4 4

:0 be Let :0 be Let

4

22

22

22

xy

xy

yy

yx

yx