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Chapter 9: Q 39. (page 731)

In Exercises 32–47 convert the equations given in polar coordinates to rectangular coordinates.
$r = 6 \csc θ$

Short Answer

Expert verified

The required equation is $y = 6$ .

Step by step solution

01

Step 1. Given information.

The given equation in polar coordinates is:

$r = 6 \csc θ$

02

Step 2. Find the equation in rectangular coordinates.

$r = 6 \csc θ r = 6 \cdot \frac{1}{\sin θ} r \sin θ = 6 y = 6 [Since r \sin θ = y]$

Therefore, the equation in rectangular coordinates is $y = 6$ .

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Most popular questions from this chapter

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

$(6, 2 \sqrt{3})$

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

$foci (0, \pm 4), directrices y = \pm 1$

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

$y = 0$

Sketch the graphs of the equations

$r = \frac{2}{1 + 2 \cos θ}$ and $r = \frac{2}{1 + 2 \sin θ}$

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

Prove that for an ellipse or a hyperbola the eccentricity is given by

$e = \frac{the distance between the foci}{the distance between the vertices}$

See all solutions

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