Explanation Given: The equation of a conic is given as, r = 4 2 − cos θ Here, r is the radius, θ is angle. Approach: The two formulas representing the conics with eccentricity e are r = e d 1 ± e cos θ or r = e d 1 ± e sin θ …(1) Then, A conic is an ellipse when the eccentricity is e < 1 Calculation: Since, r = 4 2 − cos θ Dividing denominator and numerator by 2 r = ( 4 2 ) ( 2 2 ) − ( 1 2 ) cos θ r = 2 1 − ( 1 2 ) cos θ Compare the above equation with equation (1). Here, e = 1 2 < 1 Make a table for the values of r and θ θ 0 π 4 π 2 To determine (b) The vertex and directrix of the conic r = 4 2 − cos θ , and denote vertex and directrix in the graph. To determine (c) The center, length of the major axis and length of the minor axis of the conic r = 4 2 − cos θ .

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN: 9781305071742

Author: James Stewart, Lothar Redlin, Saleem Watson

Publisher: Cengage Learning

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Question

Chapter 12.6, Problem 21E

To determine

(a)

To show:

The given conic r=42−cosθ is an ellipse and plot its graph.

To determine

(b)

The vertex and directrix of the conic r=42−cosθ, and denote vertex and directrix in the graph.

To determine

(c)

The center, length of the major axis and length of the minor axis of the conic r=42−cosθ.

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Chapter 12.6, Problem 20E

Chapter 12.6, Problem 22E

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Chapter 12 Solutions

Algebra and Trigonometry (MindTap Course List)

Ch. 12.1 - A parabola is the set of all points in the plane...Ch. 12.1 - Prob. 2E Ch. 12.1 - Prob. 3E Ch. 12.1 - Prob. 4E Ch. 12.1 - Prob. 5E Ch. 12.1 - Prob. 6E Ch. 12.1 - 5-10 Graphs of Parabolas Match the equation with...Ch. 12.1 - Prob. 8E Ch. 12.1 - 5-10 Graphs of Parabolas Match the equation with...Ch. 12.1 - Prob. 10E

Knowledge Booster

(a) To show: The given conic r = 4 2 − cos θ is an ellipse and plot its graph.

Solution Summary: The author explains that the conic r=42-mathrmcostheta is an ellipse and plots its graph.

(a)

To show:

The given conic r=42−cosθ is an ellipse and plot its graph.

(b)

The vertex and directrix of the conic r=42−cosθ, and denote vertex and directrix in the graph.

(c)

The center, length of the major axis and length of the minor axis of the conic r=42−cosθ.

Want to see the full answer?

Chapter 12 Solutions

(a) To show: The given conic r = 4 2 − cos θ is an ellipse and plot its graph.

Solution Summary: The author explains that the conic r=42-mathrmcostheta is an ellipse and plots its graph.

(a) To show: The given conic r=42−cosθ is an ellipse and plot its graph.

(b) The vertex and directrix of the conic r=42−cosθ, and denote vertex and directrix in the graph.

(c) The center, length of the major axis and length of the minor axis of the conic r=42−cosθ.

Want to see the full answer?

Chapter 12 Solutions

(a)

To show:

The given conic r=42−cosθ is an ellipse and plot its graph.

(b)

The vertex and directrix of the conic r=42−cosθ, and denote vertex and directrix in the graph.

(c)

The center, length of the major axis and length of the minor axis of the conic r=42−cosθ.