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Chapter 10: Q 26. (page 683)

Convert each polar equation into a rectangular equation.

r=31-sin(胃)

Short Answer

Expert verified

The rectangular equation is

x2-6y=9

Step by step solution

01

Step 1. Given information

The polar equation is

r=31-sin(胃)

02

Step 2. Convert into the polar equation

The polar equation is

r=31-sin(胃)

Multiply denominator on both sides

r脳(1-sin(胃))=3(1-sin(胃))脳(1-sin(胃))r脳(1-sin(胃))=3r-rsin(胃)=3

Apply conversion equation formula

r=x2+y2,y=rsin(胃)

So, the rectangular equation is

x2+y2-y=3

03

Step 3. Remove square root

The polar equation is

x2+y2-y=3

Add both sides y

x2+y2-y+y=3+yx2+y2=3+y

Take square on both sides

(x2+y2)2=(3+y)2 x2+y2=9+6y+y2x2+y2-y2-6y=9x2-6y=9

So, the rectangular equation is

x2-6y=9

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Most popular questions from this chapter

In Problems 43鈥�52, identify the graph of each equation without applying a rotation of axes.

3x2-2xy+y2+4x+2y-1=0

In Problems 43鈥�52, identify the graph of each equation without applying a rotation of axes.

2x2-3xy+2y2-4x-2=0

Find an equation for each ellipse. Graph the equation by hand.

Center at (-3,1): vertex at (-3,3): focus at(-3,0)

The Double-angle Formula for the sine function issin2胃=_______.

True or False

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