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Chapter 9: Q 38. (page 731)

In Exercises 32–47 convert the equations given in polar coordinates to rectangular coordinates.
$r = - 3 \sec θ$

Short Answer

Expert verified

The required equation is $x = - 3$ .

Step by step solution

01

Step 1. Given information.

The given equation in polar coordinates is:

$r = - 3 \sec θ$

02

Step 2. Find the equation in rectangular coordinates.

$r = - 3 \sec θ r = - 3 \cdot \frac{1}{\cos θ} r \cos θ = - 3 x = - 3 [Since r \cos θ = x]$

Therefore, the equation in rectangular coordinates is $x = - 3$ .

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Most popular questions from this chapter

Sketch the graphs of the equations

$r = \frac{2}{2 + \cos θ}$ and localid="1649860998050" $r = \frac{2}{2 + \sin θ}$

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

Complete the square to describe the conics in Exercises $18 - 21$ .

role="math" localid="1649636875685" $4 x + y^{2} - 6 y - 3 = 0$

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

$(3, 4)$

In Exercises 48–55 convert the equations given in rectangular coordinates to equations in polar coordinates.

$y = m x$

Explain why there are infinitely many different ellipses with the same foci.

See all solutions

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