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Chapter 10: Q 33. (page 683)

Convert each polar equation into a rectangular equation.

r(3-2sin(胃))=6

Short Answer

Expert verified

The rectangular equation is

9x2+5y2-24y=36

Step by step solution

01

Step 1. Given information

The polar equation is

r(3-2sin(胃))=6

02

Step 2. Convert into the rectangular equation

The polar equation is

r(3-2sin(胃))=6

Multiply ron left side

3r-2rsin(胃)=6

Apply the conversion formula

r=x2+y2,y=rsin(胃)

3x2+y2-2y=6

Add both sides 2y

3x2+y2-2y+2y=6+2y3x2+y2=6+2y

Take square on both sides and simplify

(3x2+y2)2=(6+2y)2 9(x2+y2)=36+4y2+24y9x2+9y2=36+4y2+24y9x2+9y2-4y2-24y=369x2+5y2-24y=36

So, the rectangular equation is

9x2+5y2-24y=36

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