Equations Of Circles Worksheet - Chapter 10-8 Page 5
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6AERODYNAMICS
For Exercises 35–37, use the following information.
The graph shows cross sections of spherical sound waves produced by a supersonic
airplane. When the radius of the wave is 1 unit, the plane is 2 units from the origin.
A wave of radius 3 occurs when the plane is 6 units from the center.
y
( 1, 0 )
( 6, 0 )
( 14, 0 )
( 3, 0 )
O
( 7, 0 )
x
( 2, 0 )
35. Write the equation of the circle when the plane is 14 units from the center.
36. What type of circles are modeled by the cross sections?
37. What is the radius of the circle for a plane 26 units from the center?
2
2
38. The equation of a circle is (x
6)
(y
2)
36. Determine whether the line
y
2x
2 is a secant, a tangent, or neither of the circle. Explain.
2
2
39. The equation of a circle is x
y
4x
8y
16. Find the center and radius of
the circle.
40.
WEATHER
The geographic center of Tennessee is near Murfreesboro. The
closest Doppler weather radar is in Nashville. If Murfreesboro is designated as
the origin, then Nashville has coordinates ( 58, 55), where each unit is one mile.
If the radar has a radius of 80 miles, write an equation for the circle that
represents the radar coverage from Nashville.
41.
RESEARCH
Use the Internet or other materials to find the closest Doppler
radar to your home. Write an equation of the circle for the radar coverage if
your home is the center.
42.
SPACE TRAVEL
Apollo 8 was the first manned spacecraft to orbit the moon at
an average altitude of 185 kilometers above the moon’s surface. Determine an
equation to model a single circular orbit of the Apollo 8 command module if the
radius of the moon is 1740 kilometers. Let the center of the moon be at the
origin.
CRITICAL THINKING
43.
Determine the coordinates of any intersection point of the
graphs of each pair of equations.
2
2
a. x
y
9, y
x
3
Space Travel
2
2
2
2
b. x
y
25, x
y
9
The Apollo program was
designed to successfully
2
2
2
2
c. (x
3)
y
9, (x
3)
y
9
land a man on the moon.
The first landing was July
WRITING IN MATH
44.
Answer the question that was posed at the beginning
20, 1969. There were a
of the lesson.
total of six landings on the
What kind of equations describe the ripples of a splash?
moon during 1969–1972.
Source:
Include the following in your answer:
• the general form of the equation of a circle, and
• the equations of five ripples if each ripple is 3 inches farther from the center.
Lesson 10-8 Equations of Circles 579
NASA
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