Calculus, Single Variable: Early Transcendentals (3rd Edition)
3rd Edition
ISBN: 9780134766850
Author: William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher: PEARSON
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Question
Chapter 12.4, Problem 86E
To determine
To derive: The equation of the hyperbola.
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Calculus, Single Variable: Early Transcendentals (3rd Edition)
Ch. 12.1 - Identify the graph generated by the parametric...Ch. 12.1 - Prob. 2QCCh. 12.1 - Prob. 3QCCh. 12.1 - Prob. 4QCCh. 12.1 - Prob. 5QCCh. 12.1 - Prob. 6QCCh. 12.1 - Explain how a pair of parametric equations...Ch. 12.1 - Prob. 2ECh. 12.1 - Prob. 3ECh. 12.1 - Prob. 4E
Ch. 12.1 - Prob. 5ECh. 12.1 - Prob. 6ECh. 12.1 - Prob. 7ECh. 12.1 - Prob. 8ECh. 12.1 - Prob. 9ECh. 12.1 - Prob. 10ECh. 12.1 - Prob. 11ECh. 12.1 - Prob. 12ECh. 12.1 - Prob. 13ECh. 12.1 - Prob. 14ECh. 12.1 - Prob. 15ECh. 12.1 - Prob. 16ECh. 12.1 - Prob. 17ECh. 12.1 - Prob. 18ECh. 12.1 - Prob. 19ECh. 12.1 - Prob. 20ECh. 12.1 - Prob. 21ECh. 12.1 - Prob. 22ECh. 12.1 - Prob. 23ECh. 12.1 - Prob. 24ECh. 12.1 - Prob. 25ECh. 12.1 - Prob. 26ECh. 12.1 - Prob. 27ECh. 12.1 - Prob. 28ECh. 12.1 - Prob. 29ECh. 12.1 - Prob. 30ECh. 12.1 - Eliminating the parameter Eliminate the parameter...Ch. 12.1 - Prob. 32ECh. 12.1 - Prob. 33ECh. 12.1 - Prob. 34ECh. 12.1 - Prob. 35ECh. 12.1 - Prob. 36ECh. 12.1 - Parametric equations of circles Find parametric...Ch. 12.1 - Parametric equations of circles Find parametric...Ch. 12.1 - Parametric equations of circles Find parametric...Ch. 12.1 - Parametric equations of circles Find parametric...Ch. 12.1 - Prob. 41ECh. 12.1 - Prob. 42ECh. 12.1 - Curves to parametric equations Give a set of...Ch. 12.1 - Prob. 44ECh. 12.1 - Prob. 45ECh. 12.1 - Curves to parametric equations Find parametric...Ch. 12.1 - Prob. 47ECh. 12.1 - Prob. 48ECh. 12.1 - Prob. 49ECh. 12.1 - Prob. 50ECh. 12.1 - Prob. 51ECh. 12.1 - Prob. 52ECh. 12.1 - Circular motion Find parametric equations that...Ch. 12.1 - Circular motion Find parametric equations that...Ch. 12.1 - Circular motion Find parametric equations that...Ch. 12.1 - Prob. 56ECh. 12.1 - Prob. 57ECh. 12.1 - More parametric curves Use a graphing utility to...Ch. 12.1 - More parametric curves Use a graphing utility to...Ch. 12.1 - Prob. 60ECh. 12.1 - Prob. 61ECh. 12.1 - Prob. 62ECh. 12.1 - Implicit function graph Explain and carry out a...Ch. 12.1 - Prob. 64ECh. 12.1 - Prob. 65ECh. 12.1 - Prob. 66ECh. 12.1 - Prob. 67ECh. 12.1 - Prob. 68ECh. 12.1 - Derivatives Consider the following parametric...Ch. 12.1 - Prob. 70ECh. 12.1 - Prob. 71ECh. 12.1 - Prob. 72ECh. 12.1 - Tangent lines Find an equation of the line tangent...Ch. 12.1 - Prob. 74ECh. 12.1 - Tangent lines Find an equation of the line tangent...Ch. 12.1 - Tangent lines Find an equation of the line tangent...Ch. 12.1 - Slopes of tangent lines Find all the points at...Ch. 12.1 - Slopes of tangent lines Find all the points at...Ch. 12.1 - Prob. 79ECh. 12.1 - Prob. 80ECh. 12.1 - Arc length Find the arc length of the following...Ch. 12.1 - Arc length Find the arc length of the following...Ch. 12.1 - Arc length Find the arc length of the following...Ch. 12.1 - Arc length Find the arc length of the following...Ch. 12.1 - Arc length Find the arc length of the following...Ch. 12.1 - Arc length Find the arc length of the following...Ch. 12.1 - Prob. 87ECh. 12.1 - Prob. 88ECh. 12.1 - Prob. 89ECh. 12.1 - Prob. 90ECh. 12.1 - Prob. 91ECh. 12.1 - Prob. 92ECh. 12.1 - Prob. 93ECh. 12.1 - Parametric equations of ellipses Find parametric...Ch. 12.1 - Prob. 95ECh. 12.1 - Prob. 96ECh. 12.1 - Prob. 97ECh. 12.1 - Prob. 98ECh. 12.1 - Prob. 99ECh. 12.1 - Beautiful curves Consider the family of curves...Ch. 12.1 - Prob. 101ECh. 12.1 - Prob. 102ECh. 12.1 - Area under a curve Suppose the function y = h(x)...Ch. 12.1 - Area under a curve Suppose the function y = h(x)...Ch. 12.1 - Prob. 105ECh. 12.1 - Prob. 106ECh. 12.1 - Prob. 107ECh. 12.1 - Prob. 108ECh. 12.1 - Prob. 109ECh. 12.1 - Prob. 110ECh. 12.1 - Prob. 111ECh. 12.1 - Prob. 112ECh. 12.1 - Prob. 113ECh. 12.1 - Prob. 114ECh. 12.2 - Which of the following coordinates represent the...Ch. 12.2 - Prob. 2QCCh. 12.2 - Prob. 3QCCh. 12.2 - Prob. 4QCCh. 12.2 - Prob. 5QCCh. 12.2 - Prob. 6QCCh. 12.2 - Prob. 1ECh. 12.2 - Prob. 2ECh. 12.2 - Prob. 3ECh. 12.2 - Prob. 4ECh. 12.2 - Prob. 5ECh. 12.2 - Prob. 6ECh. 12.2 - Prob. 7ECh. 12.2 - Prob. 8ECh. 12.2 - Prob. 9ECh. 12.2 - Prob. 10ECh. 12.2 - Prob. 11ECh. 12.2 - Prob. 12ECh. 12.2 - Prob. 13ECh. 12.2 - Prob. 14ECh. 12.2 - Prob. 15ECh. 12.2 - Prob. 16ECh. 12.2 - Prob. 17ECh. 12.2 - Prob. 18ECh. 12.2 - Prob. 19ECh. 12.2 - Prob. 20ECh. 12.2 - Prob. 21ECh. 12.2 - Prob. 22ECh. 12.2 - Rader Airplanes are equipped with transponders...Ch. 12.2 - Prob. 24ECh. 12.2 - Converting coordinates Express the following polar...Ch. 12.2 - Prob. 26ECh. 12.2 - Converting coordinates Express the following polar...Ch. 12.2 - Converting coordinates Express the following polar...Ch. 12.2 - Converting coordinates Express the following polar...Ch. 12.2 - Prob. 30ECh. 12.2 - Converting coordinates Express the following...Ch. 12.2 - Prob. 32ECh. 12.2 - Prob. 33ECh. 12.2 - Prob. 34ECh. 12.2 - Converting coordinates Express the following...Ch. 12.2 - Prob. 36ECh. 12.2 - Prob. 37ECh. 12.2 - Prob. 38ECh. 12.2 - Prob. 39ECh. 12.2 - Prob. 40ECh. 12.2 - Prob. 41ECh. 12.2 - Prob. 42ECh. 12.2 - Prob. 43ECh. 12.2 - Prob. 44ECh. 12.2 - Prob. 45ECh. 12.2 - Prob. 46ECh. 12.2 - Prob. 47ECh. 12.2 - Prob. 48ECh. 12.2 - Cartesian-to-polar coordinates Convert the...Ch. 12.2 - Prob. 50ECh. 12.2 - Prob. 51ECh. 12.2 - Cartesian-to-polar coordinates Convert the...Ch. 12.2 - Prob. 53ECh. 12.2 - Prob. 54ECh. 12.2 - Prob. 55ECh. 12.2 - Prob. 56ECh. 12.2 - Graphing polar curves Graph the following...Ch. 12.2 - Prob. 58ECh. 12.2 - Prob. 59ECh. 12.2 - Prob. 60ECh. 12.2 - Prob. 61ECh. 12.2 - Graphing polar curves Graph the following...Ch. 12.2 - Graphing polar curves Graph the following...Ch. 12.2 - Prob. 64ECh. 12.2 - Prob. 65ECh. 12.2 - Prob. 66ECh. 12.2 - Prob. 67ECh. 12.2 - Prob. 68ECh. 12.2 - Prob. 69ECh. 12.2 - Using a graphing utility Use a graphing utility to...Ch. 12.2 - Prob. 71ECh. 12.2 - Prob. 72ECh. 12.2 - Prob. 73ECh. 12.2 - Prob. 74ECh. 12.2 - Prob. 75ECh. 12.2 - Using a graphing utility Use a graphing utility to...Ch. 12.2 - Prob. 77ECh. 12.2 - Prob. 78ECh. 12.2 - Prob. 79ECh. 12.2 - Prob. 80ECh. 12.2 - Prob. 81ECh. 12.2 - Prob. 82ECh. 12.2 - Prob. 83ECh. 12.2 - Prob. 84ECh. 12.2 - Navigating A plane is 150 miles north of a radar...Ch. 12.2 - Prob. 86ECh. 12.2 - Prob. 87ECh. 12.2 - Prob. 88ECh. 12.2 - Prob. 89ECh. 12.2 - Prob. 90ECh. 12.2 - Prob. 91ECh. 12.2 - Prob. 92ECh. 12.2 - Prob. 93ECh. 12.2 - Prob. 94ECh. 12.2 - Prob. 95ECh. 12.2 - Prob. 96ECh. 12.2 - Prob. 97ECh. 12.2 - Prob. 98ECh. 12.2 - Prob. 99ECh. 12.2 - Prob. 100ECh. 12.2 - Prob. 101ECh. 12.2 - Spirals Graph the following spirals. Indicate the...Ch. 12.2 - Prob. 103ECh. 12.2 - Spirals Graph the following spirals. Indicate the...Ch. 12.2 - Prob. 105ECh. 12.2 - Prob. 106ECh. 12.2 - Prob. 107ECh. 12.2 - Prob. 108ECh. 12.2 - Prob. 109ECh. 12.2 - Prob. 110ECh. 12.2 - Prob. 111ECh. 12.3 - Verify that if y = f() sin , then y'() =f'() sin ...Ch. 12.3 - Prob. 2QCCh. 12.3 - Prob. 3QCCh. 12.3 - Prob. 4QCCh. 12.3 - Prob. 1ECh. 12.3 - Prob. 2ECh. 12.3 - Prob. 3ECh. 12.3 - Prob. 4ECh. 12.3 - Prob. 5ECh. 12.3 - Find a polar equation of the line with slope 1...Ch. 12.3 - Prob. 7ECh. 12.3 - Prob. 8ECh. 12.3 - Prob. 9ECh. 12.3 - Prob. 10ECh. 12.3 - Prob. 11ECh. 12.3 - Prob. 12ECh. 12.3 - Slopes of tangent lines Find the slope of the line...Ch. 12.3 - Prob. 14ECh. 12.3 - Prob. 15ECh. 12.3 - Prob. 16ECh. 12.3 - Slopes of tangent lines Find the slope of the line...Ch. 12.3 - Prob. 18ECh. 12.3 - Prob. 19ECh. 12.3 - Prob. 20ECh. 12.3 - Tangent line at the origin Find the polar equation...Ch. 12.3 - Tangent line at the origin Find the polar equation...Ch. 12.3 - Prob. 23ECh. 12.3 - Prob. 24ECh. 12.3 - Horizontal and vertical tangents Find the points...Ch. 12.3 - Prob. 26ECh. 12.3 - Horizontal and vertical tangents Find the points...Ch. 12.3 - Prob. 28ECh. 12.3 - Prob. 29ECh. 12.3 - Prob. 30ECh. 12.3 - Prob. 31ECh. 12.3 - Prob. 32ECh. 12.3 - Areas of regions Make a sketch of the region and...Ch. 12.3 - Areas of regions Make a sketch of the region and...Ch. 12.3 - Areas of regions Make a sketch of the region and...Ch. 12.3 - Areas of regions Make a sketch of the region and...Ch. 12.3 - Areas of regions Make a sketch of the region and...Ch. 12.3 - Areas of regions Make a sketch of the region and...Ch. 12.3 - Areas of regions Make a sketch of the region and...Ch. 12.3 - Prob. 40ECh. 12.3 - Intersection points and area a. Find all the...Ch. 12.3 - Intersection points and area a. Find all the...Ch. 12.3 - Prob. 43ECh. 12.3 - Intersection points and area a. Find all the...Ch. 12.3 - Prob. 45ECh. 12.3 - Prob. 46ECh. 12.3 - Prob. 47ECh. 12.3 - Prob. 48ECh. 12.3 - Areas of regions Make a sketch of the region and...Ch. 12.3 - Areas of regions Make a sketch of the region and...Ch. 12.3 - Areas of regions Make a sketch of the region and...Ch. 12.3 - Prob. 52ECh. 12.3 - Area of plane regions Find the areas of the...Ch. 12.3 - Area of plane regions Find the areas of the...Ch. 12.3 - Area of plane regions Find the areas of the...Ch. 12.3 - Area of plane regions Find the areas of the...Ch. 12.3 - Area of polar regions Find the area of the regions...Ch. 12.3 - Prob. 58ECh. 12.3 - Area of polar regions Find the area of the regions...Ch. 12.3 - Area of polar regions Find the area of the regions...Ch. 12.3 - Two curves, three regions Determine the...Ch. 12.3 - Prob. 62ECh. 12.3 - Arc length of polar curves Find the length of the...Ch. 12.3 - Prob. 64ECh. 12.3 - Prob. 65ECh. 12.3 - Prob. 66ECh. 12.3 - Prob. 67ECh. 12.3 - Prob. 68ECh. 12.3 - Arc length of polar curves Find the length of the...Ch. 12.3 - Prob. 70ECh. 12.3 - Prob. 71ECh. 12.3 - Prob. 72ECh. 12.3 - Prob. 73ECh. 12.3 - Prob. 74ECh. 12.3 - Prob. 75ECh. 12.3 - Prob. 76ECh. 12.3 - Prob. 77ECh. 12.3 - Prob. 78ECh. 12.3 - Prob. 79ECh. 12.3 - Area of roses Assume m is a positive integer. a....Ch. 12.3 - Prob. 81ECh. 12.3 - Prob. 82ECh. 12.3 - Prob. 83ECh. 12.3 - Prob. 84ECh. 12.3 - Grazing goat problems Consider the following...Ch. 12.3 - Prob. 86ECh. 12.3 - Prob. 87ECh. 12.4 - Prob. 1QCCh. 12.4 - Prob. 2QCCh. 12.4 - Prob. 3QCCh. 12.4 - Prob. 4QCCh. 12.4 - Prob. 5QCCh. 12.4 - Prob. 6QCCh. 12.4 - Prob. 1ECh. 12.4 - Prob. 2ECh. 12.4 - Prob. 3ECh. 12.4 - Prob. 4ECh. 12.4 - Prob. 5ECh. 12.4 - Prob. 6ECh. 12.4 - Prob. 7ECh. 12.4 - Prob. 8ECh. 12.4 - Prob. 9ECh. 12.4 - Prob. 10ECh. 12.4 - Prob. 11ECh. 12.4 - Prob. 12ECh. 12.4 - Prob. 13ECh. 12.4 - Prob. 14ECh. 12.4 - Prob. 15ECh. 12.4 - Prob. 16ECh. 12.4 - Prob. 17ECh. 12.4 - Prob. 18ECh. 12.4 - Prob. 19ECh. 12.4 - Prob. 20ECh. 12.4 - Prob. 21ECh. 12.4 - Prob. 22ECh. 12.4 - Prob. 23ECh. 12.4 - Prob. 24ECh. 12.4 - Prob. 25ECh. 12.4 - Prob. 26ECh. 12.4 - Prob. 27ECh. 12.4 - Prob. 28ECh. 12.4 - Prob. 29ECh. 12.4 - Prob. 30ECh. 12.4 - Prob. 31ECh. 12.4 - Prob. 32ECh. 12.4 - Prob. 33ECh. 12.4 - Prob. 34ECh. 12.4 - Prob. 35ECh. 12.4 - Prob. 36ECh. 12.4 - Prob. 37ECh. 12.4 - Prob. 38ECh. 12.4 - Prob. 39ECh. 12.4 - Prob. 40ECh. 12.4 - Prob. 41ECh. 12.4 - Prob. 42ECh. 12.4 - Prob. 43ECh. 12.4 - Prob. 44ECh. 12.4 - Prob. 45ECh. 12.4 - Prob. 46ECh. 12.4 - Prob. 47ECh. 12.4 - Prob. 48ECh. 12.4 - Prob. 49ECh. 12.4 - Prob. 50ECh. 12.4 - Prob. 51ECh. 12.4 - Prob. 52ECh. 12.4 - Prob. 53ECh. 12.4 - Prob. 54ECh. 12.4 - Prob. 55ECh. 12.4 - Prob. 56ECh. 12.4 - Prob. 57ECh. 12.4 - Prob. 58ECh. 12.4 - Prob. 59ECh. 12.4 - Prob. 60ECh. 12.4 - Prob. 61ECh. 12.4 - Prob. 62ECh. 12.4 - Tracing hyperbolas and parabolas Graph the...Ch. 12.4 - Tracing hyperbolas and parabolas Graph the...Ch. 12.4 - Tracing hyperbolas and parabolas Graph the...Ch. 12.4 - Prob. 66ECh. 12.4 - Prob. 67ECh. 12.4 - Prob. 68ECh. 12.4 - Prob. 69ECh. 12.4 - Prob. 70ECh. 12.4 - Prob. 71ECh. 12.4 - Prob. 72ECh. 12.4 - Prob. 73ECh. 12.4 - Prob. 74ECh. 12.4 - Prob. 75ECh. 12.4 - Prob. 76ECh. 12.4 - Prob. 77ECh. 12.4 - The ellipse and the parabola Let R be the region...Ch. 12.4 - Prob. 79ECh. 12.4 - Prob. 80ECh. 12.4 - Prob. 81ECh. 12.4 - Prob. 82ECh. 12.4 - Prob. 83ECh. 12.4 - Prob. 84ECh. 12.4 - Prob. 85ECh. 12.4 - Prob. 86ECh. 12.4 - Prob. 87ECh. 12.4 - Prob. 88ECh. 12.4 - Prob. 89ECh. 12.4 - Focal chords A focal chord of a conic section is a...Ch. 12.4 - Focal chords A focal chord of a conic section is a...Ch. 12.4 - Focal chords A focal chord of a conic section is a...Ch. 12.4 - Prob. 93ECh. 12.4 - Prob. 94ECh. 12.4 - Prob. 95ECh. 12.4 - Prob. 96ECh. 12.4 - Prob. 97ECh. 12.4 - Prob. 98ECh. 12 - Explain why or why not Determine whether the...Ch. 12 - Prob. 2RECh. 12 - Prob. 3RECh. 12 - Eliminating the parameter Eliminate the parameter...Ch. 12 - Prob. 5RECh. 12 - Prob. 6RECh. 12 - Prob. 7RECh. 12 - Prob. 8RECh. 12 - Prob. 9RECh. 12 - Prob. 10RECh. 12 - Prob. 11RECh. 12 - Prob. 12RECh. 12 - Prob. 13RECh. 12 - Prob. 14RECh. 12 - Prob. 15RECh. 12 - Prob. 16RECh. 12 - Prob. 17RECh. 12 - Prob. 18RECh. 12 - Prob. 19RECh. 12 - Prob. 20RECh. 12 - Prob. 21RECh. 12 - Prob. 22RECh. 12 - Prob. 23RECh. 12 - Prob. 24RECh. 12 - Prob. 25RECh. 12 - Prob. 26RECh. 12 - Prob. 27RECh. 12 - Prob. 28RECh. 12 - Prob. 29RECh. 12 - Prob. 30RECh. 12 - Prob. 31RECh. 12 - Prob. 32RECh. 12 - Prob. 33RECh. 12 - Prob. 34RECh. 12 - Prob. 35RECh. 12 - Prob. 36RECh. 12 - Prob. 37RECh. 12 - Prob. 38RECh. 12 - Prob. 39RECh. 12 - Slopes of tangent lines a. Find all points where...Ch. 12 - Slopes of tangent lines a. Find all points where...Ch. 12 - Prob. 42RECh. 12 - Prob. 43RECh. 12 - Prob. 44RECh. 12 - Prob. 45RECh. 12 - Prob. 46RECh. 12 - Prob. 47RECh. 12 - Prob. 48RECh. 12 - The area that is inside the cardioid r = 1 + cos ...Ch. 12 - Prob. 50RECh. 12 - Prob. 51RECh. 12 - Prob. 52RECh. 12 - Prob. 53RECh. 12 - Prob. 54RECh. 12 - Prob. 55RECh. 12 - Prob. 56RECh. 12 - Prob. 57RECh. 12 - Prob. 58RECh. 12 - Prob. 59RECh. 12 - Prob. 60RECh. 12 - Prob. 61RECh. 12 - Prob. 62RECh. 12 - Prob. 63RECh. 12 - Prob. 64RECh. 12 - Prob. 65RECh. 12 - Prob. 66RECh. 12 - Prob. 67RECh. 12 - Prob. 68RECh. 12 - Prob. 69RECh. 12 - Prob. 70RECh. 12 - Prob. 71RECh. 12 - Prob. 72RECh. 12 - Prob. 73RECh. 12 - Prob. 74RECh. 12 - Lam curves The Lam curve described by...Ch. 12 - Prob. 76RE
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- CONCEPTS A Hyperbola is the set of all points in the plane for which the of the distances from two fixed points F1 and F2 is constant. The point F1 and F2 are called the of the hyperbola.arrow_forwardNavigation 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).arrow_forwardNavigation 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 hyperbolic path with coordinates x,75 (see figure). (a) 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). (b) Determine the distance between the port and station A. (c) Find a linear equation that approximates the ship’s path as it travels far away from the shore.arrow_forward
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