Homework Help is Here – Start Your Trial Now!
Math
Geometry
Which intersection forms a parabola? A plane intersects only one nappe of a double-napped cone, and the plane is not parallel to the generating line of the cone. O A plane intersects both nappes of a double-napped cone, and the plane does not intersect the vertex. O A plane intersects only one nappe of a double-napped cone, and the plane is perpendicular to the axis of the cone. O A plane intersects only one nappe of a double-napped cone, and the plane is parallel to the generating line of the cone. 1 2 3 4 5 6 7 8 9 Next > 12.com/leamx-svc/getIndex/token/64760469b495148c94448cda_f1679067-1ae7-45e4-bbb9-f62ba21c65ad/conceptld/MTH2068_Stride_Geometry_08_08_Posttest/conceptType/ASSESSMENT/k12Calmsid/39

Which intersection forms a parabola? A plane intersects only one nappe of a double-napped cone, and the plane is not parallel to the generating line of the cone. O A plane intersects both nappes of a double-napped cone, and the plane does not intersect the vertex. O A plane intersects only one nappe of a double-napped cone, and the plane is perpendicular to the axis of the cone. O A plane intersects only one nappe of a double-napped cone, and the plane is parallel to the generating line of the cone. 1 2 3 4 5 6 7 8 9 Next > 12.com/leamx-svc/getIndex/token/64760469b495148c94448cda_f1679067-1ae7-45e4-bbb9-f62ba21c65ad/conceptld/MTH2068_Stride_Geometry_08_08_Posttest/conceptType/ASSESSMENT/k12Calmsid/39

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
See similar textbooks
icon
Related questions
Question
### Understanding Parabolic Intersections #### Question: Which intersection forms a parabola? #### Answer Choices: A. A plane intersects only one nappe of a double-napped cone, and the plane is not parallel to the generating line of the cone. B. A plane intersects both nappes of a double-napped cone, and the plane does not intersect the vertex. C. A plane intersects only one nappe of a double-napped cone, and the plane is perpendicular to the axis of the cone. D. A plane intersects only one nappe of a double-napped cone, and the plane is parallel to the generating line of the cone. #### Explanation: A parabola is formed when a plane intersects only one nappe (one half) of a double-napped cone, and the plane is not parallel to the generating line of the cone. When the intersection criteria specified in option A are met, it results in a parabolic shape. Options B, C, and D will result in different conic sections, such as ellipses, circles, or hyperbolas. This tutorial is designed to help students understand the geometric conditions required to form different conic sections, particularly parabolas. Each intersection criteria illustrate different parts referenced in conic section theory, and understanding which plane-and-cone interactions create parabolas is crucial in geometry and related fields.
Transcribed Image Text:### Understanding Parabolic Intersections #### Question: Which intersection forms a parabola? #### Answer Choices: A. A plane intersects only one nappe of a double-napped cone, and the plane is not parallel to the generating line of the cone. B. A plane intersects both nappes of a double-napped cone, and the plane does not intersect the vertex. C. A plane intersects only one nappe of a double-napped cone, and the plane is perpendicular to the axis of the cone. D. A plane intersects only one nappe of a double-napped cone, and the plane is parallel to the generating line of the cone. #### Explanation: A parabola is formed when a plane intersects only one nappe (one half) of a double-napped cone, and the plane is not parallel to the generating line of the cone. When the intersection criteria specified in option A are met, it results in a parabolic shape. Options B, C, and D will result in different conic sections, such as ellipses, circles, or hyperbolas. This tutorial is designed to help students understand the geometric conditions required to form different conic sections, particularly parabolas. Each intersection criteria illustrate different parts referenced in conic section theory, and understanding which plane-and-cone interactions create parabolas is crucial in geometry and related fields.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS