   Chapter 12.6, Problem 25E ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

#### Solutions

Chapter
Section ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742
Textbook Problem

# 25-28 Polar Equation for a Hyperbola A polar equation of a conic is given.(a) Show that the conic is a hyperbola, and sketch its graph. (b) Find the vertices and directrix, and indicate them on the graph.(c) Find the center of the hyperbola, and sketch the asymptotes. r = 8 1 + 2 cos θ

To determine

(a)

To show:

The given polar equation is a hyperbola. Also draw the graph of it.

Explanation

Given:

The given polar equation is,

r=81+2cosθ.

Approach:

The general equation of conic in polar form with one focus at origin and eccentricity e is given by as below.

r=ed1±ecosθ or r=ed1±esinθ

The conditions for different conic section for above formula follows as below.

a) It is a parabola if e=1.

b) It is an ellipse if 0<e<1.

c) It is hyperbola e>1.

Calculation:

Consider the given equation,

r=81+2cosθ

Compare above equation with general equation of a conic for eccentricity e

To determine

(b)

To find:

The vertices and directrix of hyperbola and show them on the graph.

To determine

(c)

To find:

The center and asymptotes of hyperbola and show it on the graph.

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