Chapter 10 Circles - 10.6 Equations Of Circles Worksheet Page 4
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W
E
Use the given information to write the standard
RITING
QUATIONS
equation of the circle.
The center is (0, 0), a point on the circle is (0, 3).
23.
The center is (1, 2), a point on the circle is (4, 6).
24.
25.
The center is (3, 2), a point on the circle is (5, 2).
The center is (º5, 3) and the diameter is 8.
26.
G
C
Graph the equation.
RAPHING
IRCLES
2
2
2
2
x
+ y
= 25
x
+ (y º 4)
= 1
27.
28.
2
2
2
2
(x + 3)
+ y
= 9
(x º 3)
+ (y º 4)
= 16
29.
30.
2
2
1
1
1
2
2
(x + 5)
+ (y º 1)
= 49
x º
+ y +
=
31.
32.
2
2
4
2
2
U
G
The equation of a circle is (x º 2)
+ (y + 3)
= 4. Tell
SING
RAPHS
whether each point is on the circle, in the interior of the circle, or in the
exterior of the circle.
(0, 0)
(2, º4)
(0, º3)
(3, º1)
33.
34.
35.
36.
37.
(1, º4)
38.
(2, º5)
39.
(2, 0)
40.
(2.5, º3)
C
P
In Exercises 41 and 42, use the following information.
ELL
HONES
A cellular phone network uses towers to transmit calls. Each tower transmits to a
circular area. On a grid of a city, the coordinates of the location and the radius
each tower covers are as follows (integers represent miles): Tower A is at (0, 0)
and covers a 3 mile radius, Tower B is at (5, 3) and covers a 2.5 mile radius, and
Tower C is at (2, 5) and covers a 2 mile radius.
Write the equations that represent the transmission boundaries of the towers.
41.
Graph each equation.
Tell which towers, if any, transmit to a phone located at J(1, 1), K(4, 2),
42.
L(3.5, 4.5), M(2, 2.8), or N(1, 6).
F
OCUS ON
A
PPLICATIONS
R
P
The figure at the
y
EULEAUX
OLYGONS
Fuel/air
Exhaust
right is called a Reuleaux polygon. It is not
in
E
F
out
a true polygon because its sides are not
C
straight. ¤ABC is equilateral.
43.
JD lies on a circle with center A and radius
AD. Write an equation of this circle.
1
44.
DE lies on a circle with center B and radius
D
G
A
B
Burning
Reuleaux
gas
1
x
BD. Write an equation of this circle.
triangle
expands
J
H
The remaining arcs
45.
C
ONSTRUCTION
The Wankel engine
of the polygon are constructed in the same
is an engine with a
way as JD and DE in Exercises 43 and 44.
triangular rotor that is based
Construct a Reauleaux polygon on a piece
on a Reuleaux triangle. It has
been used in sports cars,
of cardboard.
snowmobiles, and hybrid
46.
Cut out the Reauleaux polygon from Exercise 45. Roll it on its edge like a
electric vehicles.
wheel and measure its height when it is in different orientations. Explain why
APPLICATION LINK
a Reuleaux polygon is said to have constant width.
10.6 Equations of Circles
639
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