Chapter 10: Q. 19 (page 683)

In Problems 13–24, analyze each equation and graph it
$r = \frac{8}{2 - \sin θ}$

Short Answer

Expert verified

The equation represents an ellipse.

Step by step solution

Step 1. Given Information

We are given an equation

$r = \frac{8}{2 - \sin θ}$

We need to find the graph of the equation,

Step 2. Analyze the equation

Compare the given equation with $r = \frac{e p}{1 - e \sin θ}$

The given equation becomes,

$r = \frac{8}{2 - \sin θ} \cdot \frac{\frac{1}{2}}{\frac{1}{2}} r = \frac{4}{1 - \frac{1}{2} \sin θ}$

Here,

$e = \frac{1}{2} e p = 4 \Rightarrow (\frac{1}{2}) p = 4 \Rightarrow p = \frac{2}{1} (4) = 8$

Since, $e < 1$ , therefore, it is an ellipse.

Step 3. Plotting points

Now, we will calculate the points from the given equation,

$θ = 0 : r = \frac{8}{2 - \sin (0)} = \frac{8}{2 - 0} = \frac{8}{2} = 4 θ = \frac{π}{2} : r = \frac{8}{2 - \sin (\frac{π}{2})} = \frac{8}{2 - 1} = \frac{8}{1} = 8 θ = π : r = \frac{8}{2 - \sin (π)} = \frac{8}{2 - 0} = \frac{8}{2} = 4 θ = \frac{3 π}{2} : r = \frac{8}{2 - \sin (\frac{3 π}{2})} = \frac{8}{2 + 1} = \frac{8}{3} (\frac{8}{3}, \frac{3 π}{2})$

Step 4. Required graph

Plotting the points, we get the graph as,

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In Problems 13–24, analyze each equation and graph it
$r = \frac{8}{2 - \sin θ}$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Analyze the equation

Step 3. Plotting points

Step 4. Required graph

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In Problems 13–24, analyze each equation and graph itr=82-sinθ

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Analyze the equation

Step 3. Plotting points

Step 4. Required graph

One App. One Place for Learning.

Most popular questions from this chapter

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Theoretical and Mathematical Physics

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Study anywhere. Anytime. Across all devices.

In Problems 13–24, analyze each equation and graph it
$r = \frac{8}{2 - \sin θ}$