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Which of the following equations would correspond to a conic section formed when a plane intersects a cone parallel to the base? Ox² + y² = 32 + 34 Ox² = 8y 3² = 1 = 1

Which of the following equations would correspond to a conic section formed when a plane intersects a cone parallel to the base? Ox² + y² = 32 + 34 Ox² = 8y 3² = 1 = 1

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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**Question**: Which of the following equations would correspond to a conic section formed when a plane intersects a cone parallel to the base? **Options**: 1. \( x^2 + y^2 = 3^2 \) 2. \( \frac{x^2}{2^2} + \frac{y^2}{3^2} = 1 \) 3. \( x^2 = 8y \) 4. \( \frac{x^2}{2^2} - \frac{y^2}{3^2} = 1 \)
Transcribed Image Text:**Question**: Which of the following equations would correspond to a conic section formed when a plane intersects a cone parallel to the base? **Options**: 1. \( x^2 + y^2 = 3^2 \) 2. \( \frac{x^2}{2^2} + \frac{y^2}{3^2} = 1 \) 3. \( x^2 = 8y \) 4. \( \frac{x^2}{2^2} - \frac{y^2}{3^2} = 1 \)
**Question:** Which conic section is formed in the image shown? **Diagram Explanation:** The image depicts a double cone intersected by a horizontal plane. The plane cuts through both nappes of the cone, forming two symmetrical open curves. **Options:** - ○ Circle - ○ Parabola - ○ Ellipse - ○ Hyperbola The correct answer is **Hyperbola**, as it shows the intersection of a plane with both nappes of the cone, creating two separate curves.
Transcribed Image Text:**Question:** Which conic section is formed in the image shown? **Diagram Explanation:** The image depicts a double cone intersected by a horizontal plane. The plane cuts through both nappes of the cone, forming two symmetrical open curves. **Options:** - ○ Circle - ○ Parabola - ○ Ellipse - ○ Hyperbola The correct answer is **Hyperbola**, as it shows the intersection of a plane with both nappes of the cone, creating two separate curves.
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