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Chapter 9: Q. 22 (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.
$r = θ, r \leq 0$

Short Answer

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Step by step solution

Step 1. Given information

The equation of the curve:

$r = θ, r \leq 0$

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Most popular questions from this chapter

Use Cartesian coordinates to express the equations for the ellipses determined by the conditions specified in Exercises 32–37.

$foci (\pm α, 0), major axis 4 α$

In Exercises 60 and 61 we ask you to prove Theorem 9.23 for ellipses and hyperbolas

Consider the ellipse with equation $\frac{x^{2}}{A^{2}} + \frac{y^{2}}{B^{2}} = 1$ where $A > B$ . Let $F$ be the focus with coordinates $(\sqrt{A^{2} - B^{2}}, 0)$ . Let $e = \frac{\sqrt{A^{2} - B^{2}}}{A}$ and l be the vertical line with equation $x = \frac{A}{e}$ . Show that for any point P on the ellipse, $\frac{F P}{D P} = e_{'}$ , where $D$ is the point on $l$ closest to $P$ .

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

$y = x + 1$

Use Cartesian coordinates to express the equations for the ellipses determined by the conditions specified in Exercises 32–37.

$foci (0, \pm \frac{3 \sqrt{3}}{2}), minor axis 3$

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 2

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Graph the equation in the θr-plane. Label each arc of your curve with the quadrant in which the corresponding polar graph will occur.
$r = θ, r \leq 0$

Short Answer

Step by step solution

Step 1. Given information

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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=θ,r≤0

Short Answer

Step by step solution

Step 1. Given information

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Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Probability and Statistics

Mechanics Maths

Logic and Functions

Decision Maths

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Graph the equation in the θr-plane. Label each arc of your curve with the quadrant in which the corresponding polar graph will occur.
$r = θ, r \leq 0$