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Chapter 9: Q. 46 (page 772)

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

Short Answer

Expert verified

The graph will be

Step by step solution

01

Step 1. Given information.

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

02

Step 2. Comparison.

On comparing the given equation,

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

03

Step 3. Graph of the equation.

For $r = \frac{2}{1 + \cos θ}$ the eccentricity is $e = 1$ , so the graph is a parabola. The directrix will be the vertical line $x = 2$ .

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Most popular questions from this chapter

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

$r^{2} = \cos θ$

In exercise 26-30 Find a definite integral that represents the length of the specified polar curve and then find the exact value of integral

the spiral $r = e^{θ} f o r 0 \leq θ \leq 2 π$

Each of the integral in exercise 38-44 represents the area of a region in a plane use polar coordinates to sketch the region and evaluate the expression

The integral is $A = \int_{0}^{\frac{π}{2}} \sin 2 θ d θ$

Each of the integral in exercise 38-44 represents the area of a region in a plane use polar coordinates to sketch the region and evaluate the expression

The integral is $\int_{0}^{π} {(1 + \cos θ)}^{2} d θ$

Use polar coordinates to graph the conics in Exercises 44–51.

$r = \frac{2}{4 + \sin θ}$

See all solutions

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