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To form an ellipse, what is the relationship between the base of the cone and the angle of the plane that intersects the cone? O The plane is parallel to the base of the cone. O The plane may be perpendicular to the base of the cone. O The plane is at an angle that is neither parallel nor perpendicular to the base of the cone. O The plane must be at a 45° angle to the base of the cone.

To form an ellipse, what is the relationship between the base of the cone and the angle of the plane that intersects the cone? O The plane is parallel to the base of the cone. O The plane may be perpendicular to the base of the cone. O The plane is at an angle that is neither parallel nor perpendicular to the base of the cone. O The plane must be at a 45° angle to the base of the cone.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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### Understanding Conic Sections: Ellipse Formation Conic sections are the curves obtained by intersecting a cone with a plane in various ways. One particularly interesting conic section is an ellipse. Below is an example multiple-choice question aimed at understanding the relationship between the base of a cone and the angle of the plane that intersects it to form an ellipse. #### Question: To form an ellipse, what is the relationship between the base of the cone and the angle of the plane that intersects the cone? #### Options: 1. **The plane is parallel to the base of the cone.** 2. **The plane may be perpendicular to the base of the cone.** 3. **The plane is at an angle that is neither parallel nor perpendicular to the base of the cone.** 4. **The plane must be at a 45° angle to the base of the cone.** The correct relationship is explained as such: - An ellipse is formed when the intersecting plane is inclined at an angle to the base of the cone that is neither parallel nor perpendicular. This means the plane cuts across the cone in an oblique angle, creating an elongated loop shape in the intersection. Understanding how the orientation of the intersecting plane affects the shape formed can provide deep insights into the geometric properties of conic sections.
Transcribed Image Text:### Understanding Conic Sections: Ellipse Formation Conic sections are the curves obtained by intersecting a cone with a plane in various ways. One particularly interesting conic section is an ellipse. Below is an example multiple-choice question aimed at understanding the relationship between the base of a cone and the angle of the plane that intersects it to form an ellipse. #### Question: To form an ellipse, what is the relationship between the base of the cone and the angle of the plane that intersects the cone? #### Options: 1. **The plane is parallel to the base of the cone.** 2. **The plane may be perpendicular to the base of the cone.** 3. **The plane is at an angle that is neither parallel nor perpendicular to the base of the cone.** 4. **The plane must be at a 45° angle to the base of the cone.** The correct relationship is explained as such: - An ellipse is formed when the intersecting plane is inclined at an angle to the base of the cone that is neither parallel nor perpendicular. This means the plane cuts across the cone in an oblique angle, creating an elongated loop shape in the intersection. Understanding how the orientation of the intersecting plane affects the shape formed can provide deep insights into the geometric properties of conic sections.
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