   Chapter 12.6, Problem 22E ### 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

# SKILLS21-24 Polar Equation for a Ellipse A polar equation of a conic is given (a) Show that the conic is a ellipse, and sketch its graph. (b) Find the vertex and directrix, and indicate them on the graph. (c) Find the center of the ellipse and the length of the major and minor axes.22. r = 6 3 − 2 sin θ

To determine

(a).

To show:

The conic is an ellipse and the graph of the conic.

Explanation

Given:

The polar equation of the given conic is,

r=632sinθ(1)

Approach:

The standard equation of the conic is,

r=ed1±esinθ(2)

Here, e is the eccentricity of the conic, d is the distance of directrix from the focus, and (r,θ) are the polar coordinates.

The equation (2) represents a parabola if e=1, an ellipse if 0<e<1, and a hyperbola if e>1.

Calculation:

Divide the denominator and the nominator of equation (1) by 2.

To determine

(b).

To find:

The vertices and the directrix of the conic.

To determine

(c).

The center of the ellipse and the length of the major and the minor axes.

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