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Chapter 9: Q. 50 (page 772)

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

r=11-cos胃

Short Answer

Expert verified

The graph is

Step by step solution

01

Step 1. Given information.

The given equation isr=11-cos胃

02

Step 2. Comparison.

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

The eccentricitye=1eu=1u=1

03

Step 3. Graph.

Forr=11-cos胃the 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

In Exercises 24鈥�31 find all polar coordinate representations for the point given in rectangular coordinates.

3,-3

Measurements indicate that Earth鈥檚 orbital eccentricity is 0.0167and its semimajor axis is 1.00000011astronomical units.

(a) Write a Cartesian equation for Earth鈥檚 orbit.

(b) Give a polar coordinate equation for Earth鈥檚 orbit, assuming that the sun is the focus of the elliptical orbit.

Sketch the graphs of the equations

r=22+cos胃and localid="1649860998050" r=22+sin胃

What is the relationship between these graphs? What is the eccentricity of each graph?

Complete the definitions in Exercises 3-5.

Given a fixed line in the plane, called the ________, and a given fixed point called the _______, a parabola is the set of all points in the plane ________.

Use Cartesian coordinates to express the equations for the hyperbolas determined by the conditions specified in Exercises 38鈥�43.

foci(3,1)and(3,9), directrixy=4
See all solutions

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