Chapter 9: Q. 44 (page 772)

Use polar coordinates to graph the conics in Exercises 44–51.
$r = \frac{2}{1 + 3 \cos θ}$

Short Answer

Expert verified

The graph is

Step by step solution

Step 1. Given information.

$r = \frac{2}{1 + 3 \cos θ} .$ The given equation is

Step 2. Comparison.

On comparing the given equation with the standard form,

$r = \frac{e u}{1 + e \cos θ} The eccentricity e = 3 Here e u = 2 3 \cdot u = 2 \Rightarrow u = \frac{2}{3}$

Step 3. Graph of the equation.

For $r = \frac{2}{1 + 3 \cos θ}$ the eccentricity is $e = 2$ , so the graph is a hyperbola. The directrix is perpendicular to the polar axis at a distance $u = \frac{2}{3}$ units to the right of the pole. The directrix will be the vertical line $x = \frac{2}{3} .$

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Use polar coordinates to graph the conics in Exercises 44–51.
$r = \frac{2}{1 + 3 \cos θ}$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Comparison.

Step 3. Graph of the equation.

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Use polar coordinates to graph the conics in Exercises 44–51.r=21+3cosθ

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Comparison.

Step 3. Graph of the equation.

One App. One Place for Learning.

Most popular questions from this chapter

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Use polar coordinates to graph the conics in Exercises 44–51.
$r = \frac{2}{1 + 3 \cos θ}$