a. Radio signals emitted from points (8, 0) and (-8, 0) indicate that a plane is 8 mi closer to (8, 0) than to (-8, 0). Find an equation of the hyperbola that passes through the plane's location and with foci (8, 0) and (-8, 0). All units are in miles. b. At the same time, radio signals emitted from points (0, 8) and (0, -8) indicate that the plane is 4 mi farther from (0, 8) than from (0, -8). Find an equation of the hyperbola that passes through the plane's location and with foci (0, 8) and (0, -8). C. From the figure, the plane is located in the fourth quadrant of the coordinate system. Solve the system of equations defining the two hyperbolas for the point of intersection in the fourth quadrant. This is the location of the plane. Then round the coordinates to the nearest tenth of a mile.
a. Radio signals emitted from points (8, 0) and (-8, 0) indicate that a plane is 8 mi closer to (8, 0) than to (-8, 0). Find an equation of the hyperbola that passes through the plane's location and with foci (8, 0) and (-8, 0). All units are in miles. b. At the same time, radio signals emitted from points (0, 8) and (0, -8) indicate that the plane is 4 mi farther from (0, 8) than from (0, -8). Find an equation of the hyperbola that passes through the plane's location and with foci (0, 8) and (0, -8). C. From the figure, the plane is located in the fourth quadrant of the coordinate system. Solve the system of equations defining the two hyperbolas for the point of intersection in the fourth quadrant. This is the location of the plane. Then round the coordinates to the nearest tenth of a mile.
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter10: Analytic Geometry
Section10.1: The Rectangular Coordinate System
Problem 44E: By definition, a hyperbola is the locus of points whose positive difference of distances from two...
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Transcribed Image Text:a. Radio signals emitted from points (8, 0) and (-8, 0) indicate that a plane is 8 mi closer to (8, 0) than to (-8, 0). Find an
equation of the hyperbola that passes through the plane's location and with foci (8, 0) and (-8, 0). All units are in miles.
b. At the same time, radio signals emitted from points (0, 8) and (0, -8) indicate that the plane is 4 mi farther from (0, 8)
than from (0, -8). Find an equation of the hyperbola that passes through the plane's location and with foci (0, 8) and (0,
-8).
C. From the figure, the plane is located in the fourth quadrant of the coordinate system. Solve the system of equations
defining the two hyperbolas for the point of intersection in the fourth quadrant. This is the location of the plane. Then
round the coordinates to the nearest tenth of a mile.
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