Parametric Equations of a Hyperbola Show that the follow-ing parametric equations represent a part of the hyperbola ofExercise 57.x = aViy = bVi+ I

Given: x=at (1) y=bt+1 (2) Squaring on both sides of the equation (1) and…

Answered: Parametric Equations of a Hyperbola…

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter8: Polar Coordinates And Parametric Equations

Section8.4: Plane Curves And Parametric Equations

Problem 58E

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37-50 Finding the equation of a Hyperbola Find an equation for the hyperbola that satisfies the given conditions. Foci (5,0), length of transverse axis:6
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Navigation Long-distance radio navigation for aircraft and ships uses synchronized pulses transmitted by widely separated transmitting stations. These pulses travel at the speed of light (186,000 miles per second). The difference in the times of arrival of these pulses at an aircraft or ship is constant on a hyperbola having the transmitting stations as foci. Assume that two stations 300 miles apart are positioned on a rectangular coordinate system with coordinates (150,0)and (150,0)and that a ship is traveling on a path with coordinates (x,75), as shown in the figure. Find the x-coordinate of the position of the ship when the time difference between the pulses from the transmitting stations is 1000 microseconds (0.001 second).

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Parametric Equations of a Hyperbola Show that the follow- ing parametric equations represent a part of the hyperbola of Exercise 57. x = aVi y = bVi+ I