Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN: 9781305071742
Author: James Stewart, Lothar Redlin, Saleem Watson
Publisher: Cengage Learning
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Chapter C, Problem 25E
To determine
The graph of the equation of ellipse
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Algebra and Trigonometry (MindTap Course List)
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- Sonic boom The position of a sonic boom caused by the faster-than-sound aircraft is one branch of the hyperbola y2x2=25 in the coordinate system shown. How wide is the hyperbola 5 miles from its vertex?arrow_forwardSuspension Bridge In a suspension bridge the shape of the suspension cables is parabolic. The bridge shown in the figure has towers that are 600 m apart, and the lowest point of the suspension cables is 150 m below the top of the towers. Find the equation of the parabolic part of the cables, placing the origin of the coordinate system at the vertex. [Note: This equation is used to find the length of cable needed in the construction of the bridge.]arrow_forwardWading Pool You are building a wading pool that is in the shape of an ellipse. An equation for the elliptical shape of the pool, measured in feet, is x2324+y2196=1 Find the longest distance across the pool, the shortest distance, and the distance between the foci.arrow_forward
- Tour Boat A tour boat travels between two islands that are 12 miles apart (see figure). There is enough fuel for a 20-mile trip. (a) Explain why the region in which the boat can travel is bounded by an ellipse. (b) Let 0,0 represent the center of the ellipse. Find the coordinates of each island. (c) The boat travels from Island 1, past Island 2 to a vertex of the ellipse, and then to Island 2. How many miles does the boat travel? Use your answer to find the coordinates of the vertex. (d) Use the results from parts (b) and (c) to write an equation of the ellipse that bounds the region in which the boat can travel.arrow_forwardRoad Design Roads are often designed with parabolic surfaces to allow rain to drain off. A particular road is 32 feet wide and 0.4 foot higher in the center than it is on the sides (see figure). (a) Write an equation of the parabola with its vertex at the origin that models the road surface. (b) How far from the center of the road is the road surface 0.1 foot lower than the center?arrow_forwardBeam Deflection A simply supported beam (see figure) is 64 feet long and has a load at the center. The deflection of the beam at its center is 1 inch. The shape of the deflected beam is parabolic. (a) Write an equation of the parabola. (Assume that the origin is at the center of the beam.) (b) How far from the center of the beam is the deflection 12 inch?arrow_forward
- Navigation In the figure on the next page, the LORAN stations at A and B are 500 mi apart, and the ship at P receives station A’s signal 2640 microseconds (s) before it receives the signal from station B. Assuming that radio signals travel at 980ft/s , find d(P,A)d(P,B) . Find an equation for the branch of the hyperbola indicated in red in the figure. (Use miles as the unit of distance.) If A is due north of B and if P is due east of A, how far is P from A?arrow_forwardAPPLICATIONS Suspension Bridge In a suspension bridge the shape of the suspension cables is parabolic. The bridge shown in the figure has towers that are 600 m apart, and the lowest point of the suspension cables is 150 m below the top of the towers. Find the equation of the parabolic part of the cables, placing the origin of the coordinate system at the vertex. Note: This equation is used to find the length of cable needed in the construction of the bridge.arrow_forward
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Finding The Focus and Directrix of a Parabola - Conic Sections; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=KYgmOTLbuqE;License: Standard YouTube License, CC-BY