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Chapter 10: Q 25. (page 683)

Convert each polar equation into a rectangular equation.

r=11+cos(胃)

Short Answer

Expert verified

The rectangular equation is

y2+2x=1

Step by step solution

01

Step 1. Given information

The polar equation is

r=11+cos(胃)

02

Step 2. Convert into the polar equation

The polar equation is

r=11+cos(胃)

Multiply denominator both sides

r脳(1+cos(胃))=11+cos(胃)脳(1+cos(胃))r脳(1+cos(胃))=1r+rcos(胃)=1

Apply conversion equation formula

r=x2+y2x=rcos(胃)

So, the rectangular equation is

x2+y2+x=1

03

Step 3. Remove square root

The equation is

x2+y2+x=1

Subtract both sides x

localid="1647242304062" x2+y2+x-x=1-xx2+y2=1-x

Take square on both sides

localid="1647242312000" (x2+y2)2=(1-x)2x2+y2=1-2x+x2x2+y2+2x-x2=1y2+2x=1

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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.

9x2+12xy+4y2-x-y=0

The graph of a parabola is given. Match graph to its equation.

and equations of the parabola areA)y2=4xC)y2=-4xE)(y-1)2=4(x-1)G)(y-1)2=-4(x-1)B)x2=4yD)x2=-4yF)(x+1)2=4(y+1)H)(x+1)2=4(y+1)

Find the equation of the parabola described. Find the two points that define the latus rectum, and graph the equation by hand.

Focus at -2,0and directix of the line x=2.

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 Problem, identify the graph of each equation without completing the squares.

6x2+3y2-12x+6y=0
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