Chapter 10: Q 27. (page 683)

Convert each polar equation into a rectangular equation.
$r = \frac{8}{4 + 3 \sin (θ)}$

Short Answer

Expert verified

The rectangular equation is

$16 x^{2} + 7 y^{2} + 48 y = 64$

Step by step solution

Step 1. Given information

The polar equation is

$r = \frac{8}{4 + 3 \sin (θ)}$

Step 2. Convert into the polar equation

The polar equation is

$r = \frac{8}{4 + 3 \sin (θ)}$

Multiply both sides by the denominator

$r \times (4 + 3 \sin (θ)) = \frac{8}{4 + 3 \sin (θ)} \times 4 + 3 \sin (θ) r \times (4 + 3 \sin (θ)) = 8 4 r + 3 r \sin (θ) = 8$

Apply conversion equation formula

$r = \sqrt{x^{2} + y^{2}}, y = r \sin (θ)$

So, the rectangular equation is

$4 \sqrt{x^{2} + y^{2}} + 3 y = 8$

Step 3. Remove square root

The rectangular equation is

$4 \sqrt{x^{2} + y^{2}} + 3 y = 8$

Subtract both sides by $3 y$

$4 \sqrt{x^{2} + y^{2}} + 3 y - 3 y = 8 - 3 y 4 \sqrt{x^{2} + y^{2}} = 8 - 3 y$

Take square on both sides

${(4 \sqrt{x^{2} + y^{2}})}^{2} = {(8 - 3 y)}^{2} 16 (x^{2} + y^{2}) = 64 - 48 y + 9 y^{2} 16 x^{2} + 16 y^{2} + 48 y - 9 y^{2} = 64 16 x^{2} + 7 y^{2} + 48 y = 64$

So, the rectangular equation is

$16 x^{2} + 7 y^{2} + 48 y = 64$

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Convert each polar equation into a rectangular equation.
$r = \frac{8}{4 + 3 \sin (θ)}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Convert into the polar equation

Step 3. Remove square root

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Convert each polar equation into a rectangular equation.r=84+3sin(θ)

Short Answer

Step by step solution

Step 1. Given information

Step 2. Convert into the polar equation

Step 3. Remove square root

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Decision Maths

Statistics

Applied Mathematics

Calculus

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Convert each polar equation into a rectangular equation.
$r = \frac{8}{4 + 3 \sin (θ)}$