CalculusVolume2-SASG-07-05
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OpenStax Calculus Volume 2
Student Answer and Solution Guide
Chapter 7
Parametric Equations and Polar Coordinates
7.5 Conic Sections
Section Exercises
For the following exercises, determine the equation of the parabola using the information given.
255.
Focus and directrix Answer: 257.
Focus and directrix Answer: 259.
Focus and directrix Answer: 261.
Focus and directrix Answer: For the following exercises, determine the equation of the ellipse using the information given.
263.
Endpoints of major axis at and foci located at Answer: 265.
Endpoints of major axis at and foci located at Answer: 267.
Endpoints of major axis at and foci located at
OpenStax Calculus Volume 2
Student Answer and Solution Guide
Answer:
OpenStax Calculus Volume 2
Student Answer and Solution Guide
269.
Foci located at
and eccentricity of Answer: For the following exercises, determine the equation of the hyperbola using the information given.
271.
Vertices located at and foci located at Answer: 273.
Endpoints of the conjugate axis located at and foci located Answer: 275.
Vertices located at and focus located at Answer: 277.
Foci located at and eccentricity of 3
Answer: For the following exercises, consider the following polar equations of conics. Determine the eccentricity and identify the conic.
279.
Answer: parabola
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OpenStax Calculus Volume 2
Student Answer and Solution Guide
281.
Answer: ellipse
283.
Answer: hyperbola
OpenStax Calculus Volume 2
Student Answer and Solution Guide
For the following exercises, find a polar equation of the conic with focus at the origin and eccentricity and directrix as given.
285.
Answer: 287.
Answer: For the following exercises, sketch the graph of each conic. 289.
Answer:
291.
Answer:
OpenStax Calculus Volume 2
Student Answer and Solution Guide
293.
Answer:
295.
Answer:
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OpenStax Calculus Volume 2
Student Answer and Solution Guide
297.
Answer:
299.
Answer:
OpenStax Calculus Volume 2
Student Answer and Solution Guide
301.
Answer:
303.
Answer:
OpenStax Calculus Volume 2
Student Answer and Solution Guide
305.
Answer:
For the following equations, determine which of the conic sections is described.
307.
Answer: Hyperbola
309.
Answer: Ellipse
311.
Answer: Ellipse
313.
A satellite dish is shaped like a paraboloid of revolution. The receiver is to be located at the focus. If the dish is 12 feet across at its opening and 4 feet deep at its center, where should the receiver be placed?
Answer: At the point 2.25 feet above the vertex.
315.
A searchlight is shaped like a paraboloid of revolution. A light source is located 1 foot from the base along the axis of symmetry. If the opening of the searchlight is 3 feet across, find the depth.
Answer: 0.5625 feet
317.
A person is standing 8 feet from the nearest wall in a whispering gallery. If that person is at one focus and the other focus is 80 feet away, what is the length and the height at the center of the gallery?
Answer: Length is 96 feet and height is approximately 26.53 feet.
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OpenStax Calculus Volume 2
Student Answer and Solution Guide
For the following exercises, determine the polar equation form of the orbit given the length of the major axis and eccentricity for the orbits of the comets or planets. Distance is given in
astronomical units (AU).
319.
Hale-Bopp Comet: length of major axis = 525.91, eccentricity = 0.995
Answer: 321.
Jupiter: length of major axis = 10.408, eccentricity = 0.0484
Answer:
OpenStax Calculus Volume 2
Student Answer and Solution Guide
Chapter Review Exercises
True or False
. Justify your answer with a proof or a counterexample.
323.
The equations represent a hyperbola.
Answer: True.
325.
Given and if then where C is a constant.
Answer: False. Imagine For the following exercises, sketch the parametric curve and eliminate the parameter to find the Cartesian equation of the curve.
327.
Answer:
329.
Answer:
OpenStax Calculus Volume 2
Student Answer and Solution Guide
For the following exercises, sketch the polar curve and determine what type of symmetry exists, if any.
331.
Answer:
Symmetric about polar axis
For the following exercises, find the polar equation for the curve given as a Cartesian equation.
333.
Answer:
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OpenStax Calculus Volume 2
Student Answer and Solution Guide
For the following exercises, find the equation of the tangent line to the given curve. Graph both the function and its tangent line.
335.
Answer: For the following exercises, find the area of the region.
337.
Answer: For the following exercises, find the arc length of the curve over the given interval.
339.
Answer: For the following exercises, find the Cartesian equation describing the given shapes.
341.
A parabola with focus and directrix Answer:
OpenStax Calculus Volume 2
Student Answer and Solution Guide
343.
A hyperbola with vertices at and and foci at and Answer: For the following exercises, determine the eccentricity and identify the conic. Sketch the conic. 345.
Answer: , ellipse
347.
Determine the Cartesian equation describing the orbit of Pluto, the most eccentric orbit around the Sun. The length of the major axis is 39.26 AU and minor axis is 38.07 AU. What is the eccentricity?
Answer: This file is copyright 2016, Rice University. All Rights Reserved.