EXAMPLE 5 Use graphs of circles EARTHQUAKES The epicenter of an earthquake is the point on Earth's surface directly above the earthquake's origin. A seismograph can be used to determine the distance to the epicenter of an earthquake. Seismographs are needed in three different places to locate an earthquake's epicenter. Use the seismograph readings from locations A, B, and C to find the epicenter of an earthquake. • The epicenter is 7 miles away from A(-2, 2.5). • The epicenter is 4 miles away from B(4, 6). • The epicenter is 5 miles away from C(3, -2.5).
EXAMPLE 5 Use graphs of circles EARTHQUAKES The epicenter of an earthquake is the point on Earth's surface directly above the earthquake's origin. A seismograph can be used to determine the distance to the epicenter of an earthquake. Seismographs are needed in three different places to locate an earthquake's epicenter. Use the seismograph readings from locations A, B, and C to find the epicenter of an earthquake. • The epicenter is 7 miles away from A(-2, 2.5). • The epicenter is 4 miles away from B(4, 6). • The epicenter is 5 miles away from C(3, -2.5).
Advanced Engineering Mathematics
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Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Transcribed Image Text:EXAMPLE 5
Use graphs of circles
EARTHQUAKES The epicenter of an earthquake is the point on Earth's
surface directly above the earthquake's origin. A seismograph can be used to
determine the distance to the epicenter of an earthquake. Seismographs are
needed in three different places to locate an earthquake's epicenter.
Use the seismograph readings from locations A, B,
and C to find the epicenter of an earthquake.
• The epicenter is 7 miles away from A(-2, 2.5).
• The epicenter is 4 miles away from B(4, 6).
• The epicenter is 5 miles away from C(3, -2.5).
Solution
The set of all points equidistant from a given
point is a circle, so the epicenter is located on
each of the following circles.
y
-8
B
OA with center (-2, 2.5) and radius 7
OB with center (4, 6) and radius 4
A
OC with center (3, -2.5) and radius 5
2
To find the epicenter, graph the circles on a
graph where units are measured in miles. Find
the point of intersection of all three circles.
The epicenter is at about (5, 2).
I.
Why are three seismographs needed to locate an earthquake's epicenter?
(Analyze Example #5 to help your thinking.)
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