Chapter 10: Q 9. (page 683)

Identify the conic that each polar equation represents. Also, give the position of the directrix.
$r = \frac{4}{2 - 3 \sin (θ)}$

Short Answer

Expert verified

This polar equation is a hyperbola.

The equation of directrix is $y = - \frac{4}{3}$

Step by step solution

Step 1. Given information

The polar equation is

$r = \frac{4}{2 - 3 \sin (θ)}$

Step 2. Finding e and p

The polar equation is

$r = \frac{4}{2 - 3 \sin (θ)}$

Divide top and bottom by $2$

$r = \frac{\frac{4}{2}}{\frac{2}{2} - \frac{3}{2} \sin (θ)} r = \frac{2}{1 - \frac{3}{2} \sin (θ)}$

Compare with the standard polar equation

$r = \frac{e p}{1 - e \sin (θ)}$

So,

$e p = 2 e = \frac{3}{2} \frac{3}{2} \times p = 2 p = \frac{4}{3}$

Step 3. Identify the conic equation

We have got

$e = \frac{3}{2}$

so, $e = \frac{3}{2} > 1$

So, this is a hyperbola equation.

Step 4. Finding the directrix equation

The formula for the directrix equation is

$y = - p$

Plug $p = \frac{4}{3}$

So, the directrix equation is $y = - \frac{4}{3}$

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Identify the conic that each polar equation represents. Also, give the position of the directrix.
$r = \frac{4}{2 - 3 \sin (θ)}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Finding e and p

Step 3. Identify the conic equation

Step 4. Finding the directrix equation

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Identify the conic that each polar equation represents. Also, give the position of the directrix.r=42-3sin(θ)

Short Answer

Step by step solution

Step 1. Given information

Step 2. Finding e and p

Step 3. Identify the conic equation

Step 4. Finding the directrix equation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Probability and Statistics

Discrete Mathematics

Statistics

Pure Maths

Logic and Functions

Study anywhere. Anytime. Across all devices.

Identify the conic that each polar equation represents. Also, give the position of the directrix.
$r = \frac{4}{2 - 3 \sin (θ)}$