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Chapter 9: Q. 80 (page 568)

The letters r and 胃represent polar coordinates. Write each equation using rectangular coordinates (x,y).

r=4

Short Answer

Expert verified

The equation is written using rectangular coordinates as x2+y2=16.

Step by step solution

01

Step 1. Given Information

We are given an equation r=4.

We need to write the equation using rectangular coordinates.

02

Step 2. Concept Used

If P is a point with polar coordinates r,胃, the rectangular coordinates x,y of P are given by

x=rcos胃y=rsin胃

And it implies thatx2+y2=r2

03

Step 3. Convert into rectangular coordinates 

In the given equation r=4, we square both sides

r=4r2=42r2=16

Now using the relation r2=x2+y2the equation can be written as

r2=16x2+y2=16

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