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Chapter 9: Q. 23 (page 747)

Graph the equation in the θr-plane. Label each arc of your curve with the quadrant in which the corresponding polar graph will occur.

r=secθ

Short Answer

Expert verified

The graph of the equation:

Step by step solution

01

Step 1. Given information:

The equation of the curve:

r=secθ

02

Step 2. Graph the equation in θr-plane. 

The value of θlies on the horizontal axis and rlies on the vertical axis.

The graph of r=secθis:

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Most popular questions from this chapter

In exercise 26-30 Find a definite integral that represents the length of the specified polar curve and then find the exact value of integral

r=eθfor2kπ≤θ≤2(k+1)π

Measurements indicate that the orbital eccentricity of Mars is0.0935 and its semimajor axis is 1.517323951astronomical units.

(a) Write a Cartesian equation for the orbit of Mars.

(b) Do xand yhave the same meaning as in Exercise 53?

(c) Give a polar coordinate equation for the orbit of Mars, assuming that the sun is the focus of the elliptical orbit.

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

directrixx=3, focus(0,1)

In Exercises 32–47 convert the equations given in polar coordinates to rectangular coordinates.

r=-3secθ

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

r=21+3cosθ
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