Casio fx-CG10 Advanced Operation Manual page 94

Sample Solution—Geology and Earthquakes
a. Suppose one station determines that the epicenter of an earthquake is about
85 miles from the station. Find an equation for the possible location of the
epicenter.
We will establish a coordinate system with this station at the origin. The
epicenter could be anyplace on the circle with the equation
students do not know the formula for a circle, they can derive it fairly readily
from the distance formula, or, perhaps more appropriately, from the
Pythagorean Theorem.
b. A second station, 29 miles east and 21 miles north of the first station, shows
the epicenter to be about 65 miles away. Find an equation for the possible
location of the epicenter based on this information.
This too would be a circle, so we use the same origin as identified above. We
identify the
2
x ( 29 ) y (
c. Since a city south of both stations did not feel the effects until after both
stations, it is thought that the seismic waves come from north of the stations.
Using the information from both Parts a and b, identify one possible location
of the epicenter.
Since the epicenter must be on both circles, we can find an intersection point
for the two circles. From the GRAPH menu:
We have taken both equations and solved for y, choosing the positive
square root because of our knowledge that the epicenter is north of
both equations. Our two equations are:
y 85
2
y 65
Fostering Advanced Algebraic Thinking with Casio Technology
center at (29,
2 2
21 ) 65 .
2
x
2
x ( 29 ) 21
21) and our
2 2 2
x y 85
equation becomes
. If