   Chapter 12.6, Problem 18E ### 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

# SKILLS17-20 Polar Equation for a parabola A polar equation of a conic is given (a) Show that the conic is a parabola, and sketch its graph. (b) Find the vertex and directrix, and indicate them in the graph. r = 3 2 + 2 sin θ

To determine

(a)

To show:

The conic is a parabola and the graph of the conic.

Explanation

Given:

The polar equation of the given conic is,

r=32+2sinθ(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 numerator of equation (1) by 2.

r=(32)(22)+(22)sinθ=1

To determine

(b)

To find:

The vertex and directrix of the conic.

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