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Fill in the blanks to complete each of the following theorem statements:

For a0the graph of the equationr=2asinθis the...................... whose equation in rectangular coordinates is ....................

Short Answer

Expert verified

The blanks are filled in order as:

1. Circle

2.x2+y-a2=a2

Step by step solution

01

Step 1. Given information:

r=2asinθ

02

Step 2. Convert the polar equation into rectangular form.

r=2asinθr=2ayrr2=2ayx2+y2=2ayx2+y2-2ay=0x2+y2-2ay+a2=a2x2+y-a2=a2

This represents an equation of circle having center at0,aand radiusa.

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