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Chapter 9: Q. 62 (page 732)

Prove that the graph of the equation: r=ksec胃, -蟺2<胃<蟺2is a vertical line for any value of k鈮�0

Short Answer

Expert verified

The equation in rectangular form is x=k

So

It has been proved that graph of given equation is a vertical line.

Step by step solution

01

Step 1. Given information:

The polar form of equation:

r=ksec胃

-蟺2<胃<蟺2andk鈮�0

02

Step 2. Convert polar form of equation into rectangular form.

As we know the rectangular form is converted into polar form by using.

x=rcos胃y=rsin胃r=x2+y2

So,

cos胃=xrsec胃=rx

Now substitute expression of sec胃and rinto given equation.

r=ksec胃r=krxx=k

Thus the graph of the given equation is a vertical line, which is at a distance ofkunits fromyaxis.

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Most popular questions from this chapter

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