College Algebra
7th Edition
ISBN: 9781305115545
Author: James Stewart, Lothar Redlin, Saleem Watson
Publisher: Cengage Learning
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Textbook Question
Chapter 7.4, Problem 68E
DISCUS: A Family of Confocal Conics Conics that share a focus are called confocal. Consider the family of conics that have a focus at (0, 1) and a vertex at the origin, as shown in the figure.
- Find equations of two different ellipses that have these properties.
- Find equations of two different hyperbolas that have these properties.
- Explain why only one parabola satisfies these properties. Find its equation.
- Sketch the conics you found in parts (a), (b), and (c) on the same coordinate axes (for the hyperbolas, sketch the top branches only).
- How are the ellipses and hyperbolas related to the parabola?
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Chapter 7 Solutions
College Algebra
Ch. 7.1 - A parabola is the set of all points in the plane...Ch. 7.1 - The graph of the equation x2=4py is a parabola...Ch. 7.1 - The graph of the equation y2=4px is a parabola...Ch. 7.1 - Label the focus, directrix, and vertex on the...Ch. 7.1 - Prob. 5ECh. 7.1 - Prob. 6ECh. 7.1 - Graphs of Parabolas Match the equation with the...Ch. 7.1 - Prob. 8ECh. 7.1 - Prob. 9ECh. 7.1 - Prob. 10E
Ch. 7.1 - Graphing Parabolas An equation of a parabola is...Ch. 7.1 - Prob. 12ECh. 7.1 - Prob. 13ECh. 7.1 - Prob. 14ECh. 7.1 - Graphing Parabolas An equation of a parabola is...Ch. 7.1 - Prob. 16ECh. 7.1 - Prob. 17ECh. 7.1 - Prob. 18ECh. 7.1 - Graphing Parabolas An equation of a parabola is...Ch. 7.1 - Graphing Parabolas An equation of a parabola is...Ch. 7.1 - Graphing Parabolas An equation of a parabola is...Ch. 7.1 - Graphing Parabolas An equation of a parabola is...Ch. 7.1 - Graphing Parabolas An equation of a parabola is...Ch. 7.1 - Prob. 24ECh. 7.1 - Prob. 25ECh. 7.1 - Prob. 26ECh. 7.1 - Prob. 27ECh. 7.1 - Graphing Parabolas Use a graphing device to graph...Ch. 7.1 - Prob. 29ECh. 7.1 - Prob. 30ECh. 7.1 - Prob. 31ECh. 7.1 - Prob. 32ECh. 7.1 - Prob. 33ECh. 7.1 - Prob. 34ECh. 7.1 - Prob. 35ECh. 7.1 - Prob. 36ECh. 7.1 - Prob. 37ECh. 7.1 - Prob. 38ECh. 7.1 - Prob. 39ECh. 7.1 - Prob. 40ECh. 7.1 - Prob. 41ECh. 7.1 - Prob. 42ECh. 7.1 - Finding the Equation of a Parabola Find an...Ch. 7.1 - Prob. 44ECh. 7.1 - Prob. 45ECh. 7.1 - Prob. 46ECh. 7.1 - Prob. 47ECh. 7.1 - Finding the Equation of a Parabola Find an...Ch. 7.1 - Prob. 49ECh. 7.1 - Prob. 50ECh. 7.1 - Prob. 51ECh. 7.1 - Prob. 52ECh. 7.1 - Prob. 53ECh. 7.1 - Prob. 54ECh. 7.1 - Prob. 55ECh. 7.1 - Finding the Equation of a Parabola Find an...Ch. 7.1 - Prob. 57ECh. 7.1 - Prob. 58ECh. 7.1 - Prob. 59ECh. 7.1 - Prob. 60ECh. 7.1 - Parabolic Reflector A lamp with a parabolic...Ch. 7.1 - Satellite Dish A reflector for a satellite dish is...Ch. 7.1 - Suspension Bridge In a suspension bridge the shape...Ch. 7.1 - Reflecting Telescope The Hale telescope at the...Ch. 7.1 - Prob. 65ECh. 7.1 - Prob. 66ECh. 7.2 - An ellipse is the set of all points in the plane...Ch. 7.2 - The graph of the equation x2a2+y2b2=1 with a >b >...Ch. 7.2 - Prob. 3ECh. 7.2 - Label the vertices and foci on the graphs given...Ch. 7.2 - Prob. 5ECh. 7.2 - Prob. 6ECh. 7.2 - Prob. 7ECh. 7.2 - Prob. 8ECh. 7.2 - 7Graphing Ellipses An equation of an ellipse is...Ch. 7.2 - Graphing Ellipses An equation of an ellipse is...Ch. 7.2 - Graphing Ellipses An equation of an ellipse is...Ch. 7.2 - Graphing Ellipses An equation of an ellipse is...Ch. 7.2 - Graphing Ellipses An equation of an ellipse is...Ch. 7.2 - Graphing Ellipses An equation of an ellipse is...Ch. 7.2 - Graphing Ellipses An equation of an ellipse is...Ch. 7.2 - Graphing Ellipses An equation of an ellipse is...Ch. 7.2 - Graphing Ellipses An equation of an ellipse is...Ch. 7.2 - Graphing Ellipses An equation of an ellipse is...Ch. 7.2 - Graphing Ellipses An equation of an ellipse is...Ch. 7.2 - Prob. 20ECh. 7.2 - Prob. 21ECh. 7.2 - Prob. 22ECh. 7.2 - Prob. 23ECh. 7.2 - Prob. 24ECh. 7.2 - Prob. 25ECh. 7.2 - Prob. 26ECh. 7.2 - Prob. 27ECh. 7.2 - Prob. 28ECh. 7.2 - Prob. 29ECh. 7.2 - Prob. 30ECh. 7.2 - Prob. 31ECh. 7.2 - Prob. 32ECh. 7.2 - Prob. 33ECh. 7.2 - Prob. 34ECh. 7.2 - Prob. 35ECh. 7.2 - Prob. 36ECh. 7.2 - Prob. 37ECh. 7.2 - Prob. 38ECh. 7.2 - Prob. 39ECh. 7.2 - Prob. 40ECh. 7.2 - Prob. 41ECh. 7.2 - Prob. 42ECh. 7.2 - Prob. 43ECh. 7.2 - Prob. 44ECh. 7.2 - Prob. 45ECh. 7.2 - Prob. 46ECh. 7.2 - Prob. 47ECh. 7.2 - Prob. 48ECh. 7.2 - Prob. 49ECh. 7.2 - Prob. 50ECh. 7.2 - Prob. 51ECh. 7.2 - Prob. 52ECh. 7.2 - Prob. 53ECh. 7.2 - Prob. 54ECh. 7.2 - Prob. 55ECh. 7.2 - Prob. 56ECh. 7.2 - Prob. 57ECh. 7.2 - Prob. 58ECh. 7.2 - Prob. 59ECh. 7.2 - Prob. 60ECh. 7.2 - Prob. 61ECh. 7.2 - Prob. 62ECh. 7.2 - Prob. 63ECh. 7.2 - Prob. 64ECh. 7.2 - Perihelion and Aphelion The planets move around...Ch. 7.2 - Prob. 66ECh. 7.2 - Lunar Orbit For an object in an elliptical orbit...Ch. 7.2 - Plywood Ellipse A carpenter wishes to construct an...Ch. 7.2 - Sunburst Window A “sunburst” window above a...Ch. 7.2 - Prob. 70ECh. 7.2 - DISCUSS: Light Cone from a Flashlight A flashlight...Ch. 7.2 - DISCUSS: Is It an Ellipse? A piece of paper is...Ch. 7.3 - A hyperbola is the set of all points in the plane...Ch. 7.3 - Prob. 2ECh. 7.3 - The graph of the equation x2a2+y2b2=1 with a > 0,...Ch. 7.3 - Prob. 4ECh. 7.3 - Prob. 5ECh. 7.3 - Prob. 6ECh. 7.3 - Prob. 7ECh. 7.3 - Prob. 8ECh. 7.3 - Graphing Hyperbolas An equation of a hyperbola is...Ch. 7.3 - Graphing Hyperbolas An equation of a hyperbola is...Ch. 7.3 - Graphing Hyperbolas An equation of a hyperbola is...Ch. 7.3 - Graphing Hyperbolas An equation of a hyperbola is...Ch. 7.3 - Graphing Hyperbolas An equation of a hyperbola is...Ch. 7.3 - Graphing Hyperbolas An equation of a hyperbola is...Ch. 7.3 - Graphing Hyperbolas An equation of a hyperbola is...Ch. 7.3 - Prob. 16ECh. 7.3 - Prob. 17ECh. 7.3 - Prob. 18ECh. 7.3 - Prob. 19ECh. 7.3 - Prob. 20ECh. 7.3 - Prob. 21ECh. 7.3 - Prob. 22ECh. 7.3 - Prob. 23ECh. 7.3 - Prob. 24ECh. 7.3 - Prob. 25ECh. 7.3 - Prob. 26ECh. 7.3 - Prob. 27ECh. 7.3 - Prob. 28ECh. 7.3 - Prob. 29ECh. 7.3 - Prob. 30ECh. 7.3 - Prob. 31ECh. 7.3 - Prob. 32ECh. 7.3 - Prob. 33ECh. 7.3 - Prob. 34ECh. 7.3 - Prob. 35ECh. 7.3 - Prob. 36ECh. 7.3 - Prob. 37ECh. 7.3 - Prob. 38ECh. 7.3 - Prob. 39ECh. 7.3 - Prob. 40ECh. 7.3 - Prob. 41ECh. 7.3 - Prob. 42ECh. 7.3 - Prob. 43ECh. 7.3 - Prob. 44ECh. 7.3 - Prob. 45ECh. 7.3 - Prob. 46ECh. 7.3 - Prob. 47ECh. 7.3 - Prob. 48ECh. 7.3 - Prob. 49ECh. 7.3 - Prob. 50ECh. 7.3 - Perpendicular Asymptotes Show that the asymptotes...Ch. 7.3 - Prob. 52ECh. 7.3 - Prob. 53ECh. 7.3 - Prob. 54ECh. 7.3 - Prob. 55ECh. 7.3 - Navigation In the figure on the next page, the...Ch. 7.3 - Comet Trajectories Some comets, such as Halley’s...Ch. 7.3 - Ripples in Pool Two stones are dropped...Ch. 7.3 - Prob. 59ECh. 7.3 - DISCUSS: Light from a Lamp The light from a lamp...Ch. 7.4 - Suppose we want to graph an equation in x and y....Ch. 7.4 - Prob. 2ECh. 7.4 - Prob. 3ECh. 7.4 - Prob. 4ECh. 7.4 - Prob. 5ECh. 7.4 - Prob. 6ECh. 7.4 - Prob. 7ECh. 7.4 - Prob. 8ECh. 7.4 - Prob. 9ECh. 7.4 - Prob. 10ECh. 7.4 - Prob. 11ECh. 7.4 - Prob. 12ECh. 7.4 - Prob. 13ECh. 7.4 - Prob. 14ECh. 7.4 - Prob. 15ECh. 7.4 - Prob. 16ECh. 7.4 - Prob. 17ECh. 7.4 - Prob. 18ECh. 7.4 - Prob. 19ECh. 7.4 - Prob. 20ECh. 7.4 - Prob. 21ECh. 7.4 - Prob. 22ECh. 7.4 - Prob. 23ECh. 7.4 - Prob. 24ECh. 7.4 - Prob. 25ECh. 7.4 - Prob. 26ECh. 7.4 - Prob. 27ECh. 7.4 - Prob. 28ECh. 7.4 - Prob. 29ECh. 7.4 - Prob. 30ECh. 7.4 - Prob. 31ECh. 7.4 - Prob. 32ECh. 7.4 - Prob. 33ECh. 7.4 - Prob. 34ECh. 7.4 - Prob. 35ECh. 7.4 - Prob. 36ECh. 7.4 - Prob. 37ECh. 7.4 - Prob. 38ECh. 7.4 - Prob. 39ECh. 7.4 - Prob. 40ECh. 7.4 - Prob. 41ECh. 7.4 - Prob. 42ECh. 7.4 - Prob. 43ECh. 7.4 - Prob. 44ECh. 7.4 - Prob. 45ECh. 7.4 - Prob. 46ECh. 7.4 - Prob. 47ECh. 7.4 - Prob. 48ECh. 7.4 - Prob. 49ECh. 7.4 - Prob. 50ECh. 7.4 - Prob. 51ECh. 7.4 - Prob. 52ECh. 7.4 - Prob. 53ECh. 7.4 - Prob. 54ECh. 7.4 - Prob. 55ECh. 7.4 - Prob. 56ECh. 7.4 - Prob. 57ECh. 7.4 - Prob. 58ECh. 7.4 - Prob. 59ECh. 7.4 - Prob. 60ECh. 7.4 - Prob. 61ECh. 7.4 - Prob. 62ECh. 7.4 - Prob. 63ECh. 7.4 - Prob. 64ECh. 7.4 - Prob. 65ECh. 7.4 - Prob. 66ECh. 7.4 - Orbit of a Satellite A satellite is in an...Ch. 7.4 - DISCUS: A Family of Confocal Conics Conics that...Ch. 7 - Prob. 1CCCh. 7 - Prob. 2CCCh. 7 - Prob. 3CCCh. 7 - Prob. 4CCCh. 7 - Prob. 5CCCh. 7 - Prob. 1ECh. 7 - Graphing Parabola An equation of a parabola is...Ch. 7 - Prob. 3ECh. 7 - Prob. 4ECh. 7 - Prob. 5ECh. 7 - Prob. 6ECh. 7 - Prob. 7ECh. 7 - Prob. 8ECh. 7 - Prob. 9ECh. 7 - Prob. 10ECh. 7 - Prob. 11ECh. 7 - Prob. 12ECh. 7 - Prob. 13ECh. 7 - Prob. 14ECh. 7 - Prob. 15ECh. 7 - Prob. 16ECh. 7 - Prob. 17ECh. 7 - Prob. 18ECh. 7 - Prob. 19ECh. 7 - Prob. 20ECh. 7 - Prob. 21ECh. 7 - Prob. 22ECh. 7 - Prob. 23ECh. 7 - Prob. 24ECh. 7 - Prob. 25ECh. 7 - Prob. 26ECh. 7 - Prob. 27ECh. 7 - Prob. 28ECh. 7 - Prob. 29ECh. 7 - Prob. 30ECh. 7 - Prob. 31ECh. 7 - Prob. 32ECh. 7 - Prob. 33ECh. 7 - Prob. 34ECh. 7 - Prob. 35ECh. 7 - Prob. 36ECh. 7 - Prob. 37ECh. 7 - Prob. 38ECh. 7 - Prob. 39ECh. 7 - Prob. 40ECh. 7 - Prob. 41ECh. 7 - Prob. 42ECh. 7 - Prob. 43ECh. 7 - Prob. 44ECh. 7 - Prob. 45ECh. 7 - Prob. 46ECh. 7 - Prob. 47ECh. 7 - Prob. 48ECh. 7 - Prob. 49ECh. 7 - Prob. 50ECh. 7 - Prob. 51ECh. 7 - Prob. 52ECh. 7 - Prob. 53ECh. 7 - Prob. 54ECh. 7 - Prob. 55ECh. 7 - Prob. 56ECh. 7 - Prob. 57ECh. 7 - Prob. 58ECh. 7 - Prob. 59ECh. 7 - Prob. 60ECh. 7 - Prob. 61ECh. 7 - Prob. 62ECh. 7 - Prob. 63ECh. 7 - Prob. 64ECh. 7 - Prob. 65ECh. 7 - LORAN A ship is located 40 mi from a straight...Ch. 7 - Prob. 67ECh. 7 - Prob. 68ECh. 7 - Prob. 1TCh. 7 - Prob. 2TCh. 7 - Prob. 3TCh. 7 - Prob. 4TCh. 7 - Find an equation for the ellipse with foci (3,0)...Ch. 7 - Find an equation for the hyperbola with foci (0,5)...Ch. 7 - Prob. 7TCh. 7 - Prob. 8TCh. 7 - Prob. 9TCh. 7 - Prob. 10TCh. 7 - Prob. 11TCh. 7 - Prob. 12TCh. 7 - Find an equation for the ellipse with center (2,...Ch. 7 - Prob. 14TCh. 7 - A parabolic reflector for a car headlight forms a...Ch. 7 - Prob. 1PCh. 7 - Prob. 2PCh. 7 - Prob. 3PCh. 7 - Prob. 4PCh. 7 - Prob. 5PCh. 7 - Prob. 6P
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