Equations Of Circles Worksheet - Chapter 10-8 Page 2
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1
2
3
4
5
6Other information about a circle can be used to find the equation of the circle.
Use Characteristics of Circles
Example
Example
2
2
A circle with a diameter of 14 has its center in the third quadrant. The lines
y
1 and x
4 are tangent to the circle. Write an equation of the circle.
Sketch a drawing of the two tangent lines.
y
1
y
Since d
14, r
7. The line x
4 is
O
perpendicular to a radius. Since x
4 is
x
4
x
is a vertical line, the radius lies on a
horizontal line. Count 7 units to the left
from x
4. Find the value of h.
7 units
h
4
7 or
3
7 units
Likewise, the radius perpendicular to the
line y
1 lies on a vertical line. The
( 3,
8 )
value of k is 7 units down from
1.
k
1
7 or
8
The center is at ( 3,
8), and the radius
is 7. An equation for the circle is
2
2
(x
3)
(y
8)
49.
GRAPH CIRCLES
You can analyze the equation of a circle to find information
that will help you graph the circle on a coordinate plane.
Study Tip
Graph a Circle
Example
Example
3
3
2
2
Graphing
a. Graph (x
2)
(y
3)
16.
Calculator
Compare each expression in the equation to the standard form.
To use the center and
2
2
2
2
h)
k)
(x
(x
2)
(y
(y
3)
radius to graph a circle,
y
select a suitable window
x
h
x
y
k
y
2
3
that contains the center of
h
k
2
3
the circle. For a TI-83 Plus,
( 2, 3 )
press
ZOOM
5.
h
2
k
3
Then use 9: Circle (
2
r
16, so r
4.
on the Draw menu. Put
The center is at ( 2, 3), and the radius is 4.
in the coordinates of the
O
Graph the center. Use a compass set at a width
center and then the radius
x
so that the screen shows
of 4 grid squares to draw the circle.
“Circle ( 2, 3, 4)”.
2
2
ENTER
b. Graph x
y
9.
Then press
.
Write the equation in standard form.
y
2
2
2
(x
0)
(y
0)
3
The center is at (0, 0), and the radius is 3.
Draw a circle with radius 3, centered at
O
x
the origin.
If you know three points on the circle, you can find the center and radius of the
circle and write its equation.
576 Chapter 10 Circles
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