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Chapter 9: Q. 50 (page 772)

Use polar coordinates to graph the conics in Exercises 44–51.

r=11-cosθ

Short Answer

Expert verified

The graph is

Step by step solution

01

Step 1. Given information.

The given equation isr=11-cosθ

02

Step 2. Comparison.

On comparing the equation to standard form r=eu1+ecosθ,

The eccentricitye=1eu=1u=1

03

Step 3. Graph.

Forr=11-cosθthe eccentricity is e=1, so the graph is a parabola. The directrix is perpendicular to the polar axis at a distance u=23units to the right of the pole. The directrix will be the vertical line x=23.

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Most popular questions from this chapter

Find a definite integral expression that represents the area of the given region in polar plane and then find the exact value of the expression

The region inside the circlex2+y2=1andrightoftheverticallinex=12

in exercise 31-36 find a definite integral that represents the length of the specified polar curve, and then use graphing calculator or computer algebra system to approximate the value of integral

One petal of the polar roser=cos4θ

Use Cartesian coordinates to express the equations for the parabolas determined by the conditions specified in Exercises 22–31.

directrixy=y0, focusx1,y1, wherey0≠y1

Complete the square to describe the conics in Exercises 18–21 .

y2-8y-4x2-8x-13=0

In exercises 31-36 find a definite integral that represents the length of the specified polar curve, and then use a graphing calculator or computer algebra system to approximate the value of integral

Onepetalofthepolarroser=cos2θ
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