Circles
Learning 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



Center
Radi us
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
The equation of circle centered at
(0,0) and with radius r
Solution:
Let P(x, y) represent any point on the circle

1
P
y
0.5
x
2 +
y
2
=r
2
P
-2
x
-1
-0.5
P
-1
-1.5
1
P
2
Finding the Equation of a
Circle
The center is (0, 0) The radius is
The equation is:
x 2 + y 2 = 144
12
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
x  y 1
2
2
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
x2+y2=9
Radius of 3
Leftmost 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?
(3, 6 )
( 2, 4 )
( 2, 6 )
Find the x and y intercepts
algebraically.
x y 4
2
2
Let x be 0 :
y2  4
y2   4
y  2
Let y be 0 :
y2  4
x2   4
x  2