PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)
8th Edition
ISBN: 9781337904285
Author: Larson
Publisher: CENGAGE L
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Question
Chapter 9.1, Problem 116E
To determine
To describe in words how a plane could intersect the double-napped cone to form the
Expert Solution & Answer
Answer to Problem 116E
(a) Circle: If the plane cuts the cone such that the plane is perpendicular to the central axis, then the primary conic generated a circle.
(b) Ellipse: If the plane cuts the cone such that the plane is neither perpendicular nor parallel to axis, and the angle of intersection is greater than the generator angle, then the primary conic generated is an ellipse.
(c) Parabola: If the plane cuts the cone such that the plane is parallel to the generator, then the primary conic generated is a parabola.
(d) Hyperbola: If the plane cuts the cone such that the angle of intersection is less than the generated angle, then the primary conic generated is a hyperbola. In this case, the cutting plane intersect both nappes of the cone.
Explanation of Solution
Given information:
- Circle
- Ellipse
- Parabola
- hyperbola
To describe in words how a plane could intersect the double-napped cone to form the conic section are
(e) Circle: If the plane cuts the cone such that the plane is perpendicular to the central axis, then the primary conic generated a circle.
(f) Ellipse: If the plane cuts the cone such that the plane is neither perpendicular nor parallel to axis, and the angle of intersection is greater than the generator angle, then the primary conic generated is an ellipse.
(g) Parabola: If the plane cuts the cone such that the plane is parallel to the generator, then the primary conic generated is a parabola.
(h) Hyperbola: If the plane cuts the cone such that the angle of intersection is less than the generated angle, then the primary conic generated is a hyperbola. In this case, the cutting plane intersect both nappes of the cone.
Chapter 9 Solutions
PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)
Ch. 9.1 - Prob. 1ECh. 9.1 - Prob. 2ECh. 9.1 - Prob. 3ECh. 9.1 - Prob. 4ECh. 9.1 - Prob. 5ECh. 9.1 - Prob. 6ECh. 9.1 - Prob. 7ECh. 9.1 - Prob. 8ECh. 9.1 - Prob. 9ECh. 9.1 - Prob. 10E
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